I was browsing the forum as of late and rather surprised that this hasn't been asked before, so here it goes:
Let's say Lajos II of Hungary survives the Battle of Mohács. He is still defeated by the Ottomans, and things play out more or less as in OTL and he ends up with a rump Kingdom of Hungary. He has a son with Maria of Austria who has succeeded him in Bohemia and Hungary--we'll call him 'Vladislav III'.
Then, in 1572, King Zygmunt II August of Poland dies without issue, also as in OTL. Vladislav III (or Lajos II, if he is still alive) is now heir to the Polish throne in this scenario. Let's say he manages to secure the Crown there. This leaves him as King of Hungary, Poland and Bohemia, and Grand Duke of Lithuania. How would this play out and what would be the effects?
If Vladislav III is savy, astute, and, let's be honest, somewhat lucky, would he be able to secure this inheritance and found establish himself as a European power?
I've always liked the idea of a surviving Jagiellon dynasty...