A convenient omission, Oli, although Michael, at his party, told Vincent that "Mr. Joe Zasa now owns what used to be the Corleone Family business in New York." A bit earlier, before Vincent joined them, Michael told Zasa: Joe, your business is your business. I have no interests or percentage – I’m out." So, it is arguable that Michael didn't care who succeeded Zasa.
A more serious omission: Who took over the Corleone Family, which was still under Michael's control in II, after Pentangeli flipped and the Rosato brothers were on the run?
My theory is that Mike is still running the family as a criminal enterprise after Part 2. The last scene in part 2 is suppose to take place in 1968 when Anthony goes off to college and basically shuns Mike. Mike still has that cold look in his eyes so I'm sure he is still a cold blooded mobster at that point. My guess is that sometime in the early 70's Mike finally gives up Control of the criminal family to Zasa
