Each center has their own skill set, and that is what sets them apart.
However, to be a good center, you must be able to rebound the ball, box out your opponent, score in the post, and hit a mid range jump shot. Most centers in the league can do this; the best can do all of them well, along with being a force on the inside on the defensive end (blocking shots, as well).
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Overall, it takes a lot of team play and hustle, not only in practice, but also on the court. You should also have good instincts (which comes from practicing hours and hours and hours) and the ability to be versatile.
Well he (or she) has to be a good leader, but the most important thing is that he/she has to have a huge knowledge of Basketball