@EatYerGreens: For faction leaders, they increase their faction's income by roughly 2% per feather of Acumen. (Acumen and Dread work much the same way in this regard.) That's why when a king dies, you probably notice a drop in your income, but that it's not necessarily a drastic difference.

Quote Originally Posted by Peasant Phill
What influences the amount of influence (no pun intended) a heir gets when he is coronated?

Is it the heirs stats? The amount of provinces under his control? The influence of the old king? all of the above?
That's a darn good question, Phill. If you can figure that one out, then you're definitely smarter than me -- not that that would take much.

As best I can tell, it's mostly affected by the old king's influence combined with the number of provinces you own. Whether the new king's stats affect his influence as well, it wouldn't entirely surprise me. I've never managed to detect any direct correlation between the two, however.