  Recent observations show a strong correlation between stellar mass and
accretion rate in young stellar and sub-stellar objects, with the scaling
$\dot{M}_{acc} \propto M_*^2$ holding over more than four orders of magnitude
in accretion rate. We explore the consequences of this correlation in the
context of disk evolution models. We note that such a correlation is not
expected to arise from variations in disk angular momentum transport efficiency
with stellar mass, and suggest that it may reflect a systematic trend in disk
initial conditions. In this case we find that brown dwarf disks initially have
rather larger radii than those around more massive objects. By considering disk
evolution, and invoking a simple parametrization for a shut-off in accretion at
the end of the disk lifetime, we show that such models predict that the scatter
in the stellar mass-accretion rate relationship should increase with increasing
stellar mass, in rough agreement with current observations.
