What is the most important aspect of a basketball center's conditioning?

The most important aspect of a basketball training program should be determined by a self-appraisal of your weaknesses and strengths. Whatever attribute is holding you back should be your priority while training.  For example, although most critics will comment on a center's strength and power, it may be your conditioning that stands between you and the next level of play.  Just think of how many open baskets you could get if you beat the opposing players down the court every time.

As an adjunct to the previous answer, a center's conditioning should be should be at a high level.  Interval based conditioning with specifically timed rest intervals, will help to simulate game conditions and allow for the athlete to perform at a high level for a longer duration.