I will make short comment for Croatia which I am familiar with to illustrate example

First is Croatia. In early 9th century Charlemagne broke power of Avars, in area of today Croatia which was until that time under Avar sphere, he founded two vassal duchies. This area was particullary important for him due to the proximity of Byzantium, so he created those two duchies as buffer states. One of those was Duchy of Croatia situated in area which is today known as Dalmatia.

We have few sources to draw on for duchy of Damlatia, but what is clear that early dukes who were unrelated to each other were appointed by kings of Franks. How did they come of power? Well early sources speak of powerful groups of armed men serving as their bodyguards. So to become duke you had to rely on powerfull group of allies which later on you had to reward for you service and then gain approval of Frankish king. Keep in mind that it that feudalism would come to this area much later on. Due to the weakining of Frankish power dukes started to become much more independent. Around middle 9th century duke named Trpimir took throne and managed to rule long enough to gain legitimacy for his sons who were considered good enough candidates to succeed him instead of random noble. But powerfull unrelated noble Domagoj soon after his death took throne with strenght of his arms. After his death son of Trpimir Zdeslav came to power but due to his Byzanthophile politics he soon was ousted by another powerfull unrelated noble named Branimir. But after Branimir had died, second son of Trpimir Mutimir took throne and power remained concentrated in hands of Trpmir´s progeny. It was not easy ride after that because it was not clear how power should be divided if ruler had multiple sons which often lead to civil wars.

As said there are no much sources, but it seems that power shifted to hands of one specific family due to its prestige and its willingness to give supportes some kind of reward who in turn supported son of previous ruler in order to continue reaping benefits.

Neven Budak, Tomislav Raukar Hrvatska povijest srednjeg vijeka 2006.

Danijel Džino Becoming Slav, Becoming Croat: Identity transformations in post-Roman Dalmatia. 2010.