Dynamical mean field methods are used to calculate the phase diagram, many-body density of states, relative orbital occupancy and Fermi surface shape for a realistic model of $LaNiO_3$-based superlattices. The model is derived from density functional band calculations and includes oxygen orbitals. The combination of the on-site Hunds interaction and charge-transfer between the transition metal and the oxygen orbitals is found to reduce the orbital polarization far below the levels predicted either by band structure calculations or by many-body analyses of Hubbard-type models which do not explicitly include the oxygen orbitals. The findings indicate that heterostructuring is unlikely to produce one band model physics and demonstrate the fundamental inadequacy of modeling the physics of late transition metal oxides with Hubbard-like models.
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