Large Cuman population in Europe/Cuman nation

The Cumans were a large steppe confederacy which played a great role in medieval Central and Eastern Europe and the Balkans. They were destroyed by the Mongol invasion, which supplanted them on the steppe. Many Cumans (tens of thousands) settled in Hungary and eventually converted to Catholicism. Two regions of Hungary, Great Cumania and Little Cumania, were so named because of their large Cuman population which was afforded various rights until the 19th century.

Linguistically, the Cumans in Europe died out, and culturally they blended into the European nations they settled. So what I'm asking is how do we get a large Cuman population--at least as big as the Gagauz (who if they aren't descendents of the Cumans, probably have Cuman ancestry amongst other Turkic groups) of Moldova. There should be at least one region of some European country where the majority of the population is Cuman. If there can be a Cuman country, that would be even better.

My thought is that a stronger Mongol invasion of Europe (where they conquer Hungary) could depopulate a portion of Hungary--ideally Transylvania, and the area settled by Cumans as well as other steppe peoples like Tatars. Over time, the population of Cumans, who adopt Christianity, assimilate the other groups and eventually settle down (as the OTL Cumans in Hungary did). The region is thus majority Cuman, and may or not form the core of an independent Cuman-speaking country at some point in the future.

Thoughts?
 
Doesn't Great Cumania have lots of Cuman ancestry? Isn't it like the 4th biggest contributor of that region genetically (which Hungarian being the greatest obviously)? Or is it not about genetics but cultural that you want (after all Austrians are descended from more Lombard speaking people than Germans... though Lombard is a Germanic language)?
 
Can we fairly count cultures with a significant Cuman/Kipchak element to their ethnogenesis? Because if so, an independent Crimean Tatar state would seem to satisfy this, at least in terms of the common language. There's a lot of things involved in that complex, but you could always handwave it with a more significant Cuman migration into the Crimean region sometime in the Middle Ages.
 
Doesn't Great Cumania have lots of Cuman ancestry? Isn't it like the 4th biggest contributor of that region genetically (which Hungarian being the greatest obviously)? Or is it not about genetics but cultural that you want (after all Austrians are descended from more Lombard speaking people than Germans... though Lombard is a Germanic language)?

All Lombards are Germans technically. And yes, the Cumans are genetically ancestors of many groups (including many noble/ruling families), but otherwise their cultural and language is dead or submerged. From what I get at, the only Cumans nowadays are basically a subgroup of Hungarians.

Can we fairly count cultures with a significant Cuman/Kipchak element to their ethnogenesis? Because if so, an independent Crimean Tatar state would seem to satisfy this, at least in terms of the common language. There's a lot of things involved in that complex, but you could always handwave it with a more significant Cuman migration into the Crimean region sometime in the Middle Ages.

Wasn't the Cuman language different/not ancestral to Crimean Tatar? And in any case with the Crimean Tatars, you'd have to convert them to Christianity for them to be part of the historic European cultural sphere...although converting them (or the Cumans in general) to Buddhism would always be cool, but rather ASB.
 
Wasn't the Cuman language different/not ancestral to Crimean Tatar? And in any case with the Crimean Tatars, you'd have to convert them to Christianity for them to be part of the historic European cultural sphere...although converting them (or the Cumans in general) to Buddhism would always be cool, but rather ASB.
As far as I know, there are a few dialects, one of the most prominent of which comes from the Kipchak-Cuman complex with some heavy influences from the dialect spoken by the Oghuz. Regardless, it'd be somewhat trivial to direct more Cumans into Crimea on their way into Europe, or have more of them migrate there ahead of the *Mongols or whoever else decides to come west.
 
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