You're right, it makes one wonder what happened after Mary's death... but do we need to know what happened to Vincent, Connie, etc.?

The Trilogy was about Michael, how his actions and decisions as Don brought to ruin his world and his relationship with his loved onces, and he paid for his sins with the death of Mary. Nothing needs to be said in between Mary's death and his own. 'What did Michael do?' after Mary's death. The terrible, terrible price that Michael paid for his actions in life haunted him forever, and drove him to dying a lonely and bitter old man. That's what happened.

'What becomes of Vinnie, Connie etc. ?' I liked Part III, but I felt one of it's chief failings was that Vincent, despite Garcia's worthy preformance, Vincent as a character, was a little under-developed. I mean, no sooner then we learn Sonny has illegitimate kid, what is done with him? Not much, we know he's a bit of a hothead and a wise guy, and desires to rise up in the family business, and is using Mary for this. But I mean... where has Vincent been all this time? Why hasn't Michael, Tom, ANYBODY, mentioned him 'till now? How did The Family react when they learnt of his existence? How many people knew? ...stuff like that. Do I care much when Vinnie becomes Don Corleone? No, as the whole time through Part III we see Michael trying to move out of that role, and Michael, when we come to Part III, hardly has the hallmarks of one who is a Don. Making Vincent the Don didn't really lift the burden of the family's crime dealings from Michael, as we saw from Mary's death. The aspect of Michael's life came back to haunt him, no matter how hard he tried to escape from it. So Vincent becoming Don wasn't that big a deal to me.

Now perhaps Vincent can be developed further in a Part IV, but it's my belief we don't NEED a Part IV, as I've explained elsewhere, and anyway, I feel Vincent's character, where we left him at the end of Part III, isn't interesting enough to carry a film alone.

And we don't need Connie where there's no Michael. Connie, like Kay, Mary, Anthony, and Vincent are characters whose sole purpose is to contribute to Michael's story in Part III, as he struggles for family legitmacy and strives for redemption. And with Michael's death, the story is over. I feel Connie, Kay etc. are no longer good and interesting characters if they are not there solely for being part of Michael's world.

Yeah, it makes one wonder what became of Vinnie up to Michael's death... but it's not essential information IMO.