The Rulers of Vinland (1070-1600)
Ulfir I Snorrisson, King of Vinland (1070-1104)
Ulfr Snorrason
Tarr I Ulfirsson, King of Vinland (1104-1138)
Tarr Ulfsson (Tarr? ??? where did you get that?)
Ulfir II Tarrsson, Called the Viking, King of Vinland & Greenland (1138-1150)
Ulfr Tarsson (probably, depends on what the root of 'Tarr' is)
Snorri I Ulfirsson, King of Vinland & Greenland (1150-1174)
Snorri Ulfsson
Ulfir III Snorrisson, Called the Savior, King of Vinland (1174-1203)
Ulfr Snorrason
Tarr II Ulfirsson, Called the Killer, King of Vinland & Harvior (1203-1236)
The War of the Three Kings (1236-1244): Heimir Ulfirsson, Ulfir Ulfirsson, Tarr Ulfirsson, none succeed to the throne - Heimir's son Snorri succeeds for lack of population.
Snorri II Heimirsson, Called the New Blood, King of Vinland & Harvior (1244-1261)
Ulfir IV Snorrisson, King of Vinland & Harvior (1261-1285)
Ulfir V Ulfirsson, Called the Second, King of Vinland & Harvior (1285-1299)
Snorri III Ulfirsson, Called the Conciliator, King of Vinland (1299-1330)
Anna I Snorrisdottir, called the Skraeling, Queen of Vinland & Mother of the Tribes (1330-1375)
Anna? ??? A Christian name in the middle of all these Norse names?
Heimir I Syvursson, King of Vinland & Chief of the Tribes (1375-1388)
Heimir?? Syvur??
Syvur I Heimirsson, Called the Teacher, King of Vinland & Chief of the Tribes (1388-1407)
Ulfir VI Syvursson, King of Vinland & Chief of the Tribes (1407-1415)
The Black Years (1415-1451): Plague ruins the kingdom and savages North America. Decades pass without a ruling authority before the accession of Ulfir VII of the Tarr Branch, long removed from the main line since the 1240s.
Ulfir VII, Called the Destined, Emperor of Vinland (1451-1499)
Heimir II Ulfirsson, Emperor of Vinland (1499-1523)
Ulfir VIII, Called the Fool, Emperor of Vinland (1523-1529)
Dotta I Ulfirsdottir, called the She-Wolf, Empress of Vinland (1529-1552)
Dotta??
Ulfir VIII Bjallsson, Emperor of Vinland (1552-1583)
Bjallsson??? If he's "Dotta"s son, he'd be called that.
Syvur II Ulfirsson, Called the Patron, Emperor of Vinland (1583-1600)