Some historians have made the argument that the Ottoman Empire was just an Islamic extension of the Roman/Byzantine Empire.
Oh, and Hungarians are descended from the Huns.
Not really. The Huns were a pretty small tribe. They settled down and were assimilated by the local population. Hungarians are mostly descended from the Magyars, who came later.
Hmm, I wouldn't call the Huns a 'small tribe'. What did the Pope call them again? The scourge of God, IIRC.
And I'm sure you know in an attempt to somewhat appease the Huns, who where attacking pretty much "Rome" at will, the Eastern Emperor 'gave' the Huns a province North of the Danube River, which is now Hungary.
And as I'm sure you also know, the Goths originally occupied that land, but they were pushed South of the Danube into "Rome", by the Huns. But they were allowed access on the condition that the Goths fight as a Roman ally against the Huns. (the Goths always got screwed by Rome IMHO). In any case the Huns occupied Hungary long before the Magyars arrived around 800 AD. (but yes the word Hungary is a 'Magyar word')
And yes assimilation occurred, but that was a common occurrence 'back then'. Wherever the Roman Empire reached (Western & Eastern), assimilation occurred. Just like the Vikings did in the 800's they eventually assimilated where they went; Russia, Normandy and Briton. The only group that I can recall that didn't assimilate as a rule in Europe was the Mongols.