I've commented on this several times before. The best analogy I can post is how the Chicago Outfit ran under Tony Accardo. Tony was the power behind the throne for decades. The best known Chicago Outfit boss that operated with his approval was Sam Giancana. There was no doubt among the wiseguys in Chicago that Sam was the Outfit boss. But there was also no doubt among them that Tony could exercise ultimate control if he chose to. Joe Bonanno exercised suzerainty over the the family that carried his name (and still does) even though he was ensconced out west.

That's exactly the relationship between Mike and Clemenza and Pentangeli and Zasa. As Vincent put it, "Everyone knows you're like the Supreme Court." For whatever reason some men exercise power and are recognized by other men as having that power, Mike had it. He was an overlord of a extensive empire that included the Corleone family back in NY. He told Zasa that we have no debts, no percentages. Zasa stated that the Commission gave me that territory and you approved. But since the Corleone family carried Mike's name, he wanted to make sure that it was operated in a manner consistent with the way he thought it should. He didn't exercise operational control.

GFIII leaves us with no replacement for Zasa. We imagine it was Vinnie. But Vinnie was succeeding Michael which meant that he would inherit responsibility for a heck of alot more than just the few hundred Corleone Soldiers in NY.