Thought it would be appropriate to update family trees...I've changed things up in the Jagiellon and Aviz lines a little bit.
HOUSE OF HABSBURG
Maximilian I, Holy Roman Emperor (b. 1459, r. 1483-1501, d. 1501) m. a) Mary, Duchess of Burgundy (b. 1457, r. 1477-1482, d. 1482) in 1476, had issue; b) Bianca Maria Sforza (b. 1473) in 1494, had no issue
1a) Philip of Austria, Duke of Burgundy (b. 1478, r. 1482-1495, d. 1495)
2a) Margaret of Austria, Duchess of Burgundy and Queen of the Romans (b. July 1480, r. from 1495) m. Charles of Guelders, King of the Romans (previously Duke of Guelders; b. 1467) in 1497, has issue
1) Mary of Burgundy, Princess of Portugal (b. September 1498) m. Infante João, Prince of Portugal (b. 1497) in 1515, has no issue
2) Philip of Burgundy, Count of Charolais (b. April 1500) eng. Catherine of the Palatinate (b. 1499)
3) Catherine of Burgundy (b. February 1502) eng. Stephen Jagiellon of Hungary and Bohemia (b. September 1502)
4) Isabelle of Burgundy (b. August 1503)
5) John of Burgundy, Count of Hainaut (b. October 1504)
6) Agnes of Burgundy (b. March 1507)
3a) Francis of Austria (b. 1481, d. 1481)
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HOUSE OF TRASTÁMARA
Isabella I, Queen of Castile (b. 1451, r. from 1474, d. 1507) m. Ferdinand II, King of Aragon (b. 1453, r. from 1479) in 1469, has issue
1) Isabel of Aragon and Castile, Princess of Portugal (b. 1470, d. 1503) m. Afonso, Prince of Portugal (b. 1475, d. 1491) in 1490, had no issue
2) Juan of Aragon and Castile, Prince of Asturias and Girona (b. 1478, d. 1499) m. Giovanna III, Queen of Naples (b. 1478, d. 1504) in 1497, had issue
1) Ferdinand VI, King of Castile (b. 1498) m. Magdalena of Navarre (b. 1494) in 1512, has issue
1) Carlos, Prince of Viana (b. and d. 1514)
2) Charles IV, King of Naples (b. 1500) eng. Leonor of Portugal (b. 1498)
3) Juana of Aragon and Castile, Queen of Portugal (b. 1479) m. Manuel I, King of Portugal (b. 1469) in 1496, has issue
See House of Aviz for issue
4) Maria of Aragon and Castile, Queen of Hungary and Bohemia (twin of stillborn child; b. 1482) m. Vladislaus II, King of Hungary and Bohemia (b. 1467) in 1499, has issue
See House of Jagiellon (Hungary and Bohemia) for issue
5) Stillborn child (twin of Maria; b. and d. 1482)
6) Catalina of Aragon and Castile, Princess of Wales (b. 1485) m. Arthur Tudor, Prince of Wales (b. 1486) in 1502, has issue
See House of Tudor for issue
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HOUSE OF AVIZ
King Manuel I of Portugal (formerly Duke of Viseu; b. 1469, r. from 1495) m. Juana of Aragon and Castile (b. 1479) in 1496, has issue
1) João, Prince of Portugal (b. 1497) m. Mary of Burgundy (b. 1498) in 1515, has no issue
2) Leonor of Portugal (b. 1498) eng. Charles IV, King of Naples (b. 1500)
3) Afonso of Portugal (b. 1500, d. 1501)
4) Isabel of Portugal (b. 1503)
5) Beatrice of Portugal (b. 1504)
6) Fernando of Portugal, Duke of Beja (b. 1506)
7) Antonio of Portugal (b. and d. 1507)
8) Henrique of Portugal (b. 1512)
9) Duarte of Portugal (b. 1514)
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HOUSE OF TUDOR
Henry VII Tudor, King of England (formerly earl of Richmond; b. 1458, r. from 1485, d. 1514) m. Elizabeth of York (b. 1466) in 1485, has issue
1) Arthur Tudor, Prince of Wales (b. 1486, d. 1513) m. Catalina of Aragon and Castile (b. 1485) in 1502, has issue
1) Stillborn daughter (b. and d. 1503)
2) Henry Tudor (b. and d. 1504)
3) Stillborn son (b. and d. 1507)
4) Stillborn son (b. and d. 1508)
5) Edward VI Tudor, King of England (twin of Edmund; b. 1510)
6) Edmund Tudor, Duke of Richmond (twin of Edward; b. 1510)
7) Mary Tudor (b. 1513)
2) Margaret Tudor, Queen of Scots (b. 1489) m. James IV Stewart, King of Scots (b. 1473) in 1503, has issue
See House of Stewart for issue
3) Henry Tudor, Duke of York (b. 1491, d. 1551) m. Anne de La Tour d’Auvergne (b. 1494) in 1506, has issue
1) Margaret Tudor (b. 1512)
2) Stillborn son (b. and d. 1514)
4) Elizabeth Tudor (b. 1492, d. 1495)
5) Mary Tudor (b. 1496) m. Charles VIII, King of France (b. 1470) in 1514, has no issue
6) Edmund Tudor, Duke of Somerset (b. 1499, d. 1500)
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HOUSE OF VALOIS
Charles VIII, King of France (b. 1470, r. from 1477) m. Anne, Duchess of Brittany (b. 1477, r. 1488-1514, d. 1514) in 1491, has issue (a); Mary Tudor (b. 1496) in 1514, has no issue (b)
1a) Charles Orland, Dauphin of France (b. 1492, d. 1495)
2a) François of France, Duke of Normandy (b. and d. 1493)
3a) Stillborn daughter (b. and d. 1494)
4a) Stillborn daughter (b. and d. 1495)
5a) Charles, Dauphin of France (b. and d. 1496)
6a) François, Dauphin of France (b. and d. 1497)
7a) Louise of France (b. and d. 1498)
8a) Charlotte of France, Duchess of Brittany (b. 1499) m. Charles, Duke of Orléans (b. 1501) in 1515, has no issue
9a) Louis, Dauphin of France (b. and d. 1503)
10a) Anne of France (b. 1510)
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HOUSE OF SAVOY and VALOIS-ANGOULÊME/VALOIS-ORLÉANS:
Philip II, Duke of Savoy (b. 1438, r. 1496-1497, d. 1497) m. Marguerite of Bourbon (b. 1438, d. 1483) in 1472, had issue (a); Claudine de Brosse (b. 1450, d. 1513) in 1485, had issue (b)
1a) Louise of Savoy (b. 1476) m. Charles of Valois, Duke d’Angoulême (b. 1459, d. 1496) in 1489, has issue (a); Louis of Valois, Duke of Orléans and Milan (b. 1464, d. 1515) in 1499, has issue (b)
1a) Marguerite d’Angoulême, Duchess of Nemours (b. 1492) m. Gaston de Foix, Duke of Nemours (b. 1489) in 1509, has issue
1) Françoise de Foix (b. 1511)
2) Jean de Foix (b. and d. 1513)
2a) François, Duke d’Angoulême (b. 1494) m. Catherine of Navarre (b. 1495) in 1513, has issue
1) Charles d’Angoulême (b. 1514, d. 1515)
3b) Charles, Duke of Orléans (b. 1501, d. 1535) m. Charlotte of France, Duchess of Brittany (b. 1499) in 1515, has no issue
4b) Jeanne d’Orléans (b. 1502) [1] eng. Louis II, Duke of Savoy (b. 1502)
5b) Louis d’Orléans (b. and d. 1506)
6b) Philippe d’Orléans (b. 1509, d. 1512)
7b) Marie d’Orléans (b. 1510)
8b) Anne d'Orléans (b. and d. 1512)
9b) Isabelle d’Orléans (b. 1514)
2a) Girolamo of Savoy (b. and d. 1478)
3a) Philibert II, Duke of Savoy (b. 1480, r. 1497-1504, d. 1504) m. Yolande Louise of Savoy (b. 1487, d. 1499) in 1496, had no issue (a); Charlotte of Naples, Princess of Taranto (b. 1479/1480, d. 1513) in 1500, has issue (b)
1b) Philippa of Savoy (b. 1501)
2b) Louis II, Duke of Savoy (b. 1502) [2] eng. Jeanne d’Orléans (b. 1502)
3b) Anne of Savoy (b. 1504)
1b) Charles of Savoy, Count of Geneva (b. 1486)
2b) Louis of Savoy (b. 1488, d. 1502)
3b) Philip of Savoy (b. 1490)
4b) Assolone of Savoy (b. and d. 1494)
5b) Giovanni of Savoy (b. and d. 1495)
6b) Philiberta of Savoy (b. 1498)
[1] Named after her father’s ex-wife, Jeanne of France, who was also named her godmother as an act of good feeling between her parents and Jeanne.
[2] Louis is named for his godfather, the Duke of Milan and Orléans
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HOUSE OF JAGIELLON (Hungary-Bohemia)
Vladislaus II Jagiellon, King of Hungary and Bohemia (b. 1456, r. from 1471) m. Maria of Aragon and Castile (b. 1482) in 1500, has issue
1) Elisabeth Jagiellonica of Hungary and Bohemia (b. 1501)
2) Stephen Jagiellon of Hungary and Bohemia (b. 1502) eng. Catherine of Burgundy (b. 1502)
3) Anna Jagiellonica of Hungary and Bohemia (b. 1503)
4) Louis Jagiellon of Hungary and Bohemia, Duke of Slavonia (b. 1505)
5) Catherine Jagiellonica of Hungary and Bohemia (b. 1506)
6) Andrew Jagiellon of Hungary and Bohemia (b. 1509)
7) Sophia Jagiellonica of Hungary and Bohemia (b. 1512)
8) Barbara Jagiellonica of Hungary and Bohemia (b. and d. 1513)
9) Ladislaus Jagiellon of Hungary and Bohemia (b. and d. 1515)
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HOUSE OF JAGIELLON (Poland-Lithuania)
Sigismund I Jagiellon, King of Poland and Grand Duke of Lithuania (b. 1467) m. Catherine of Mecklenburg (b. 1487) in 1507, has issue
1) Sigismund Jagiellon (b. 1509, d. 1512)
2) Alexander Jagiellon (b. and d. 1511)
3) Hedwig Jagiellonica (b. 1513)
4) Sophia Jagiellonica (b. 1515)
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HOUSE OF OLDENBURG
Christian I, King of Denmark, Sweden, and Norway (b. 1426, d. 1481) m. Dorothea of Brandenburg (b. 1430/1431, d. 1495) in 1449, had issue
1) Olaf of Denmark (b. 1450, d. 1451)
2) Canute of Denmark (b. 1451, d. 1455)
3) John, King of Denmark, Sweden, and Norway (b. 1455, r. from 1481, d. 1513) m. Christina of Saxony (b. 1461) in 1478, has issue
1) Hans of Denmark and Norway (b. 1479, d. 1480)
2) Ernst of Denmark and Norway (b. 1480, d. 1500)
3) Christian II, King of Denmark and Norway (b. 1481) m. Anna of Brandenburg (b. 1487, d. 1514) in 1502, has issue
1) John, Crown Prince of Denmark and Norway (b. 1503)
2) Francis of Denmark (b. and d. 1505)
3) Dorothea of Denmark (b. 1507)
4) Jacob? (b. 1484?)
5) Elisabeth of Denmark and Norway, Electress of Brandenburg (b. 1485, d. 1555) m. Joachim I Nestor, Elector of Brandenburg (b. 1484) in 1502, has issue
Issue as IOTL
6) Francis of Denmark and Norway (b. 1497, d. 1499)
4) Margaret of Denmark, Queen of Scots (b. 1456, d. 1486) m. James III Stewart, King of Scots (b. 1451/1452, d. 1488) in 1469, had issue
See House of Stewart for issue
5) Frederick of Denmark, Duke of Schleswig-Holstein (b. 1471) m. Dorothea of Mecklenburg (b. 1480) in 1498, has issue
1) Sophia of Schleswig-Holstein (b. 1501)
2) Dorothea of Schleswig-Holstein (b. 1505)
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HOUSE OF STEWART
James III Stewart, King of Scots (b. 1451/1452, d. 1488) m. Margaret of Denmark (b. 1456, d. 1486) in 1469, had issue
1) James IV Stewart, King of Scots (b. 1473) m. Margaret Tudor (b. 1489) in 1502, has issue
1) James Stewart, Duke of Rothesay (b. 1507, d. 1508)
2) Stillborn daughter (b. and d. 1508)
3) Arthur Stewart, Duke of Rothesay (b. 1509, d. 1510)
4) James Stewart, Duke of Rothesay (b. 1512)
5) Stillborn daughter (b. and d. 1512)
6) Alexander Stewart, Duke of Ross (b. 1514, d. 1515)
7) Margaret Stewart (b. 1515)
2) James Stewart, Duke of Ross (b. 1476, d. 1504)
3) John Stewart, earl of Mar (b. 1479, d. 1503)
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HOUSE OF BORGIA
Pope Alexander VI (born Rodrigo de Borja; b. 1431, d. 1503) never married, had illegitimate issue w/Vannozza dei Cattanei (b. 1442, d. 1518)
1) Cesare Borgia, Duke of Florence, Siena, Urbino, and the Romagna (b. 1475, d. 1512) m. Giovanna of Savoy (b. 1482) in 1500, had issue
1) Lucrezia Borgia (b. 1501)
2) Rodrigo Borgia (b. 1503, d. 1512)
3) Filippo Borgia (b. 1504, d. 1512)
4) Girolama Borgia (b. 1507)
2) Juan/Giovanni Borgia, 2nd Duke of Gandia (b. 1474/1476, d. 1497) m. María Enriquez de Luna (b. 1474) in 1493, had issue
1) Juan de Borja y Enriquez, 3rd Duke of Gandia
2) Francisca de Jesús de Borja y Enriquez
3) Isabel de Borja y Enriquez
3) Lucrezia Borgia, Duchess of Ferrara (b. 1480, d. 1508) m. Giovanni Sforza, Lord of Pesaro and Gradara (b. 1466, d. 1510) in 1493, ann. 1497, had no issue (a); Alfonso d’Aragona, Duke of Bisceglie and Prince of Salerno (b. 1481, d. 1500) in 1498, had issue (b); Alfonso d’Este, Duke of Ferrara (b. 1476) in 1502, had issue (c)
1b) Rodrigo d’Aragona, Duke of Bisceglie and Prince of Salerno (b. 1499, d. 1511)
1c) Stillborn daughter (b. and d. 1502)
2c) Alessandro d’Este (b. and d. 1505)
3c) Ercole II d’Este, Duke of Ferrara (b. 1508)
4) Gioffre Borgia, Prince of Squillace (b. 1481/1482) m. Sancha d’Aragona, Princess of Squillace (b. 1478, d. 1506) in 1493, had no issue (a); Clarice de’Medici (b. 1493) in 1508, had issue (b)
1) Piero Borgia (b. 1510)
2) Lucrezia Borgia (b. 1512)
3) Alfonso Borgia (b. 1514)
4) Isabella Borgia (b. 1515)