>>21547
I'm also interested in parallels and the origin.
As a parallel, I see one in the Merovings, supposedly the Carolings should be similar but I read little about them.
But the source I'm almost sure isn't the Franks. According to legend the progenitress of the dynasty was "visited" by the Turul in her dream like how Mary was visited by the Holy Spirit which is frequently depicted as a dove or Maya by the White Elephant so this is similar to the Ashina tribe you mentioned. They had a totemistic origin myth which can be the source of their respect but the establishment of it in practice with the strict rules of inheritance isn't necessarily going back to pagan times because there is one notable break which repeats the "exception under the rule" twice, or maybe three times in a way actually.

>wha are the reasons that Bela couldnt centralize the kingdom?
It's not a wise thing to piss against the wind.
By the reign of Béla IV's father, Andrew II, a stable nobility evolved. There were no oligarchs yet but as a societal stratum they were strong, influential enough to force him to issue a golden bull - called The Golden Bull - which had similar role to the English Magna Charta which preceded it only by 7 years, wow Hungary so progressive, truly we were First World back then. Andrew also excessively awarded lands to the clerics and nobles, lands which still were the most important source of income and soldiers. To the times of Béla the strength of royal power was noticeably weak enough for him to wish to change the trends. I should note here tho that still everyone had a healthy fear of him. For example he could order that the members of his privy council - the highest notability of the realm - mustn't sit in his presence and noone dared to say him fuck you. They hated him for such petty moves but noone said nothing. However traditionally this and reclaiming of the lands awarded by his father are considered as a reason leading to lose support against the Mongols and the disaster at Muhi. Frankly the time just past the point where the trend could have been turned around and centralize.
It wasn't just too late to centralize but it was also too early too.
With the economical progress, the growing international trade other income sources opened up but things just started to pick up, wasn't enough possibilities yet to exploit to the king's favor. Those times only came by the half of the 14th century. Maybe it could have been done little earlier but the weaker kings just couldn't do anything László IV was murdered by his own subjects, an unimaginable act in previous times.

For the map:
Darker green is the domains of the first Christian king, István I.
Lighter green is the areas where the estates were predominantly his.
The uncolored regions is a mixed bag frankly, some were almost empty due hydrographical reasons, but I think most were in the hands of the clergy (and not the nobility) as it seems these were organized around episcopal seats (little circles with crosses on top of them).
This map is little misleading as around the Carpathians were very sparsely populated and uninhabited regions.