  We present cosmological N-body resimulations of the assembly of the Brightest
Cluster Galaxies (BCGs) in rich clusters. At $z=2$ we populate dark matter
subhalos with self-gravitating stellar systems whose abundance and structure
match observed high-redshift galaxies. By $z=0$, mergers have built much larger
galaxies at cluster centre. Their dark matter density profiles are shallower
than in corresponding dark-matter-only simulations, but their total mass
density profiles (stars + dark matter) are quite similar. Differences are found
only at radii where the effects of central black holes may be significant. Dark
matter density slopes shallower than $\gamma=1.0$ occur for $r/r_{200} <
0.015$, close to the half-light radii of the BCGs. Our experiments support
earlier suggestions that NFW-like profiles are an attractor for the
hierarchical growth of structure in collisionless systems -- total mass density
profiles asymptote to the solution found in dark-matter-only simulations over
the radial range where mergers produce significant mixing between stars and
dark matter. Simulated dark matter fractions are substantially higher in BCGs
than in field ellipticals, reaching 80\% within the half-light radius. We also
estimate that supermassive black hole mergers should create BCG cores as large
as $r_{c}\sim 3 \,\mathrm{kpc}$. The good agreement of all these properties
with recent observational studies of BCG structure suggests that dissipational
processes have not played a dominant role in the assembly of the observed
systems.
