Is there some kind of a chart indicating what gain/loss of influence is triggered by an event ?

I am well aware that loosing battles or provinces, failed crusades/jihads and having your agent assassinated trigger loss of influence but I have never known exactly of how much.

IS it also possible that some AI factions have some kind of almost fixed influence ? Byz emperors seems always to have at least eight in my games even when they are left with just a few provinces (Byz emperor proudly sitting in Cyprus - his single provinces - with max influence is something I have seen a quite few times)

Last question how much influence does the new king gets compared to his immediate predecessor ? When my king dies seems as if some kind of random deduction takes places (between 0 and 3). Don't know if it is correct though (or linked with the stats of the new king).