  In this paper we study physical measures for $\C^{1+\alpha}$ partially
hyperbolic diffeomorphisms with mostly expanding center. We show that every
diffeomorphism with mostly expanding center direction exhibits a
geometrical-combinatorial structure, which we call skeleton, that determines
the number, basins and supports of the physical measures. Furthermore, the
skeleton allows us to describe how physical measures bifurcate as the
diffeomorphism changes under $C^1$ topology.
  Moreover, for each diffeomorphism with mostly expanding center, there exists
a $C^1$ neighborhood, such that diffeomorphism among a $C^1$ residual subset of
this neighborhood admits finitely many physical measures, whose basins have
full volume.
  We also show that the physical measures for diffeomorphisms with mostly
expanding center satisfy exponentially decay of correlation for any H\"older
observes.
