  Starting from an abstract elementary class with no maximal models, Shelah and
Villaveces have shown (assuming instances of diamond) that categoricity implies
a superstability-like property for a certain independence relation called
nonsplitting. We generalize their result as follows: given an abstract notion
of independence for Galois (orbital) types over models, we derive that the
notion satisfies a superstability property provided that the class is
categorical and satisfies a weakening of amalgamation. This extends the
Shelah-Villaveces result (the independence notion there was splitting) as well
as a result of the first and second author where the independence notion was
coheir. The argument is in ZFC and fills a gap in the Shelah-Villaveces proof.
