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Depends on the team. I've seen parts of some of the rosters starting to be assembled already. Most of these early rosters seem to be players that were playing in extended spring training. I imagine they won't truely be set until Monday. Even then they will change(Fill out) as the weeks go on.
Alot of this is based on when these drafted players are signed and where they get placed in the organization. Typically you will see more college players start off in the NYP. But it's really all in where the organization feels the player is best suited.