I think at the point of GF3, Michael tutors Vincent and realizes he is, at that particular time, the best candidate to replace himself. Anthony wants no part of it; Vincent is willing to learn and is after all his brother's son, albeit illegitimate. Vincent grasps what he needs to learn and manages to learn to control his temper, a feat his father never accomplished. I think in this aspect of the movie, Michael is like his father in counseling and teaching patience to the young man.