Toward the end of III, while sitting beside Don Tommasino's coffin, Michael seems to anoint Vincent as his heir. Michael basically has given up. Vincent says all the wants is to preserve the family. Michael says, "Nephew, call yourself Vincent Corleone." There's a bunch of hand-kissing. Michael tells Vincent he has to give up Mary, then Vincent busies himself with organizing the assassinations of Michael's enemies. You know the rest of it.

My question: What did Michael really have i mind for Vincent, long term? Did he envision Vincent as just physical protector? Or would Vincent have a place in Immobiliare or the rest of the Corleone legitimate empire? Your thoughts?

I think he wanted to save Vincent from going down the same path he did but like you said in the end realizes It’s hopeless. Yes he wanted Vince t to be apart of the legitimate world and play a big part in Immobiliare

I think that Michael wanted Vincent to handle the criminal side of the Corleone family.

Remember when Vincent told Michael in his office that Michael's lawyers couldn't protect him, but he could? Michael took him up on it. By doing so, Michael (at least in his mind) would separate the criminal Corleones from the legitimate Corleones. Anthony and Mary would some day take over the legitimate side and Vincent would be there to provide physical security.

It didn’t seem like Mike wanted Vincent to run the criminal side. “I offered you something better in the legitimate world, you turned me down”. So even before the movie began Mike was trying to
Push Vincent into legit work

Sonny's son? I think he wanted to protect him as much as he can because of the way things turned out with Sonny.

Probably would be a consigliere (think what Vito was to Michael) and try to keep him as safe as possible. Once Vincent chose that path, I doubt Michael would go on and bring him to the legitimate world after that - he had his children to think about as well. I don't think he'd want them to be too close, as in spending a lot of time together, but close enough that if his kids ever needed "support", Vincent would be there.

I'm with Oli. Vincent acquired a bit of polish by hanging around Michael, but he was still basically muscle. I don't think he had Michael's head for the big deals (as Pentangeli described himself). I agree with Oli--the legit businesses were destined for Mary and Anthony.