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Say that Jogaila's third wife Elżbieta Granowska outlived him, thus he dies without sons and do not start new dynasty. He still have daughter from his second marriage, Jadwiga (Hedwig) born in 1408. She was engaged with Frederick Hohenzollern, born in 1413, son of Elector of Brandenburg but eventually she died unmarried in December 1431. With her brothers never born her marriage would be more important question than IOTL but say that she still dies young and childless (there were rumors that Jadwiga was poisoned by her stepmother but there is no proof for it, so let's assume that she died from natural cases).
In 1430 Grand Duke of Lithuania Vytautas died. Jogaila wanted his own brother Švitrigaila to replace him. Švitrigaila has no heir so Jogaila hoped that he'll leave Lithuanian throne to his sons. ITTL Jogaila has no sons but he could hope for GDL throne for his daughter or future grandkids so he could still support Švitrigaila (who would still have enough time to piss him off before Jadwiga's death). So would Jogaila turn his support to Žygimantas when his daughter dies and Švitrigaila's lack of heirs is no more an advantage in Jogaila's eyes? Žygimantas would propably still prevail over Švitrigaila anyway. And the winner of the struggle for Lithuanian throne is most likely candidate to get additional throne in Cracow.
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