WI: Teutons win the battle of Grunwald

I can't see the way to preserve union after king's death on battlefield. TO propaganda would for sure treat it as a sign from God that the pagan cannot succeed against God's knights. Poland would be for some period of time in disarray, though the fortifications built by Kasimir the Great wouldn't allow the knights to wint too much. They would probably try to bring Vytautas to their side promising him a support in reaching king's crown. A the same time they would try to set the other Lituanian princes against him to undermine Vytautas' reign. I think most probable course for Poland in this scenario would be to crown Ziemowit ASAP, integrate Masovia into the state and try to ally with Pomeranian princes, Danes and Swedes.
I don't know what would be Polish-Lithuanian relations in the early year after defeat. There would be probably many blaming for the folly and some boundary tensions, especially in Podolia, contested by both parties. But in the end the necessity to fight against the common enemy would probably bring some cooperation. Polish propaganda at thas time was also quite successfull and Poles probably would claim that Teutons destroy the work of Jadwiga who managed to baptize Lithuania peacefully. Both Poland and Lithuania also have more demographic potential, so if the Order is pushing too much it would find itself surrended by foes, each of them demographically dominating over Knights.
The last question is what would be papal standing in this mess. If papa supports Teutonic Order, Poles would IMO support council over pope (this of Rome, of course. They never supported pope of Avignon). But papal court always liked money from Poland and quite frequently supported polish in the past, against TO too. Papal court would also like to have secured money from Lithuania, so they would probably try to win Vytautas to their side.
Besides the times after Grunwald would be really hot and question of schizm and reformist teachings of Hus would probably distract the clergy enough to let Eastern European societes and nations lead their wars their way.
 
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