Short answer: Komnenos
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Considering game standings, for early starts (pre 1200s), any of their members make a lot of sense, gives interesting gameplay.
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Legitimacy. Interesting topic, in the entire Europe the ruling class is formed mostly out of the new arriving barbarians, who are now "civilised". Former populations with decent from Roman Empire period have a majority, but only a weak word to say in the politics.
Thus, the descendants of Constantin make little sense to me.
In the BE we have a very interesting phenomena, that will occur in the west as well. The conquered, the greek, slowly and subvertingly, they changed the aristocracy left behind by the romans with their own. And the other nations in the BE aren't going to be passive, they do the same, but in order to have legitimacy, they "become greek". I.e. in the game look at the Kometoupoulos and other "greek" families (go to family tree and check the ancestors). They have completely different backgrounds than their grandchildren. Historically this is a very common thing everywhere in Europe, even if it started a lot earlier in the BE (at least 500 years earlier). The greeks should have their own legacy (the romans didn't destroy the old greeks and neither did they ever assimilated them) in both the former greek/macedonian and in former seleucid cities.
So IMO none have legitimate descent - from a medieval perspective. However, from a nationalistic point of view, they have more claim (the greeks in Greece, armenians in Armenia and so on).
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From history after the CK2 era in the orthodox regions, I would say that the Komnenos have been viewed as the true line of emperors. The first tsar claimed legitimacy by marrying a Komnenos (hope I'm not mistaken and remember correctly). And nobles in regions with little aristocratic tradition (the vlachs, the bulgarians) have always used alliances/unions with the main or cadet branches of the Komnenos - this family more than any other - in order to justify their claims. Their legacy has echoed until the 1600-1700s (probably because of Alexios too). Because of this echo, I assume that they had or claimed to have some degree of descent into major families of the roman era too.
There are too little believable sources to get a good idea about this.
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There you have it: Komnenos.