  We investigate a hierarchical structure formation scenario in which galaxy
stellar cores are created from the binding energy liberated by shrinking
supermassive black hole (SMBH) binaries. The binary orbital decay heats the
surrounding stars, eroding a preexisting 1/r^2 stellar cusp. We follow the
merger history of dark matter halos and associated SMBHs via cosmological Monte
Carlo realizations of the merger hierarchy from early times to the present in a
LCDM cosmology. Massive black holes get incorporated through a series of
mergers into larger and larger halos, sink to the center owing to dynamical
friction, accrete a fraction of the gas in the merger remnant to become
supermassive, and form a binary system. Stellar dynamical processes drive the
binary to harden and eventually coalesce. A simple scheme is applied in which
the loss cone is constantly refilled and a constant density core forms due to
the ejection of stellar mass. We find that a model in which the effect of the
hierarchy of SMBH interactions is cumulative and cores are preserved during
galaxy mergers produces at the present epoch a correlation between the `mass
deficit' (the mass needed to bring a flat inner density profile to a 1/r^2
cusp) and the mass of the nuclear SMBH, with a normalization and slope
comparable to the observed relation. Models in which the mass displaced by the
SMBH binary is replenished after every major galaxy merger appear instead to
underestimate the mass deficit observed in `core' galaxies.
