  We prove a structure theorem for ergodic homological rotation sets of
homeomorphisms isotopic to the identity on a closed orientable hyperbolic
surface: this set is made of a finite number of pieces that are either
one-dimensional or almost convex. The latter ones give birth to horseshoes; in
the case of a zero-entropy homeomorphism we show that there exists a geodesic
lamination containing the directions in which generic orbits with respect to
ergodic invariant probabilities turn around the surface under iterations of the
homeomorphism. The proof is based on the idea of $\textit{geodesic tracking}$
of orbits that are typical for some invariant measure by geodesics on the
surface, that allows to get links between the dynamics of such points and the
one of the geodesic flow on some invariant subset of the unit tangent bundle of
the surface.
