  Accretion studies have been focused on the flow around bodies with point mass
gravitational potentials, but few general results are available for non-point
mass distributions. Here, we study the accretion flow onto non-divergent, core
potentials moving through a background medium. We use Plummer and Hernquist
potentials as examples to study gas accretion onto star clusters, dwarf and
large galaxy halos and galaxy clusters in a variety of astrophysical
environments. The general conditions required for a core potential to
collectively accrete large quantities of gas from the external medium are
derived using both simulations and analytic results. The consequences of large
mass accumulation in galaxy nuclei, dwarf galaxies and star clusters are
twofold. First, if the gas cools effectively star formation can be triggered,
generating new stellar members in the system. Second, if the collective
potential of the system is able to alter the ambient gas properties before the
gas is accreted onto the individual core members, the augmented mass supply
rates could significantly alter the state of the various accreting stellar
populations and result in an enhanced central black hole accretion luminosity.
