Hungary and Poland wins battle of Varna

What if the Hungarian and Polish armies defeated the Ottoman Army in 1444.

http://en.wikipedia.org/wiki/Battle_of_Varna

First the Papal army would chase and finish off the Ottomans, and then kick out of the continent. They would then restore lands back to the Byzantines. This would end with a roughly Greece sized Byzantine Empire. Also Wallachia, Moldova, and Serbia would be completely liberated from Ottoman rule. This would also likely lead to more Crusades against the Ottomans, and increased Papal relations with the Byzantines. In other words it would be like taking a defibrillator to the Byzantine Empire.
 
Would they really restore lands to the Byzantines though, rather than setting up Latin duchies over Greece again?

Did the Ottomans really have no reserves/significant forces left in the event of a loss at Varna?
 
I think a much more important result could be the survival of the King Ladislav and the continuation of the personal union between Poland-Lithuania-Hungary-Croatia. In such a timeline the Jagelo dynasty would probably take the place of the Habsburgs in terms of power in continental Europe.
 
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