I took this from an interview with two comic strip writers (artists?) whom I enjoy and respect, Hilary Price and Rina Piccolo.
Rina is speaking:
Anyway, the stories are centered around the theme of apartments. Or at least most of the stories are centered on apartments and apartment living. Some are based on real stuff from real life, and some are fiction.
Correct is “centered on.” The center is a point, so it can’t be around something.
I included that third sentence to point out a good technique: Don’t repeat yourself if you can help it. Maybe that’s why she used the two versions of “centered.”