  We investigate the stability of gravitational accretion of an ideal gas onto
a compact object moving through a uniform medium at Mach 3. Previous
three-dimensional simulations have shown that such accretion is not stable, and
that strong rotational 'disk-like' flows are generated and accreted on short
time scales. We re-address this problem using overset spherical grids that
provide a factor of seven improvement in spatial resolution over previous
simulations. With our higher spatial resolution we found these 3D accretion
flows remained remarkably axisymmetric. We examined two cases of accretion with
different sized accretors. The larger accretor produced very steady flow, with
the mass accretion rate varying by less than 0.02% over 30 flow times. The
smaller accretor exhibited an axisymmetric breathing mode that modulated the
mass accretion rate by a constant 20%. Nonetheless, the flow remained highly
axisymmetric with only negligible accretion of angular momentum in both cases.
