  Subject to some relatively mild assumptions, we derive the complete form of
all timelike half-supersymmetric solutions to N=2, D=4 gauged supergravity
coupled to an arbitrary number of abelian vector multiplets. This is done using
spinorial geometry techniques. Explicit examples are given for a simple
prepotential. Among the solutions, there are near-horizon geometries of
extremal rotating BPS black holes still to be discovered, with a nontrivial
dependence of the scalar fields on one of the horizon coordinates.
