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What would be needed for Charlemagne's successors to consolidate at least this area into a single state?

http://www.fsmitha.com/h3/map04chrls.htm

I imagine something like he only has one son, and then they swtich to primogeniture.

What would be the impact of this? It would control most of the good agricultural land in Europe, and could dominate states in Iberia and southern Italy.
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