The centrality dependence of elliptic flow and how it is related to the physics of expansion of the system created in high energy nuclear collisions is discussed. Since in the hydro limit the centrality dependence of elliptic flow is mostly defined by the elliptic anisotropy of the overlapping region of the colliding nuclei, and in the low density limit by the product of the elliptic anisotropy and the multiplicity, we argue that the centrality dependence of elliptic flow should be a good indicator of the degree of equilibration reached in the reaction. Then we analyze experimental data obtained at AGS and SPS energies. The observed difference in the centrality dependence of elliptic flow could imply a transition from a hadronic to a partonic nature of the system evolution. Finally we exploit the multiplicity dependence of elliptic flow to make qualitative predictions for RHIC and LHC.