I know Pepin divided the kingdom between his two sons, as Germanic peoples were often wont to do. But what was the thought process when it came to this type of succession in the long term? Surely nobody expected the kingdom to keep dividing itself forever and remain stable.
I think you mean descendants, not ancestors :)
To phrase this in a more historical context, were there cases of Frankish inheritances not being large enough for the number of sons it was to be divided amongst? What happened in these cases?