  Minor mergers of galaxies are expected to be common in a hierarchical
cosmology such as $\Lambda$CDM and have the potential to significantly affect
galactic structure. In this paper we dissect the case-by-case outcome from a
set of numerical simulations of a single satellite elliptical galaxy accreting
onto a massive elliptical galaxy. We take care to explore cosmologically
relevant orbital parameters and to set up realistic initial galaxy models that
include all three relevant dynamical components: dark matter halos, stellar
bulges, and central massive black holes. The effects of several different
parameters are considered, including orbital energy and angular momentum,
satellite density and inner density profile, satellite-to-host mass ratio, and
presence of a black hole at the center of the host. Black holes play a crucial
role in protecting the shallow stellar cores of the hosts, as satellites
merging onto a host with a central black hole are more strongly disrupted than
those merging onto hosts without black holes. Orbital parameters play an
important role in determining the degree of disruption: satellites on less
bound or more eccentric orbits are more easily destroyed than those on more
bound or more circular orbits as a result of an increased number of pericentric
passages and greater cumulative effects of gravitational shocking and tidal
stripping. In addition, satellites with densities typical of faint elliptical
galaxies are disrupted relatively easily, while denser satellites can survive
much better in the tidal field of the host. Over the range of parameters
explored, we find that the accretion of a single satellite elliptical galaxy
can result in a broad variety of changes, in both signs, in the surface
brightness profile and color of the central part of an elliptical galaxy.
