  We study ergodic properties of partially hyperbolic systems whose central
direction is mostly contracting. Earlier work of Bonatti, Viana about existence
and finitude of physical measures is extended to the case of local
diffeomorphisms. Moreover, we prove that such systems constitute a C^2-open set
in which statistical stability is a dense property. In contrast, all mostly
contracting systems are shown to be stable under small random perturbations.
