  Observations of T Tauri stars and young brown dwarfs suggest that the
accretion rates of their disks scale strongly with the central stellar mass,
approximately $\mdot \propto M_*^2$. No dependence of accretion rate on stellar
mass is predicted by the simplest version of the layered disk model of Gammie
(1996), in which non-thermal ionization of upper disk layers allows accretion
to occur via the magnetorotational instability. We show that a minor
modification of Gammie's model to include heating by irradiation from the
central star yields a modest dependence of $\mdot$ upon the mass of the central
star. A purely viscous disk model could provide a strong dependence of
accretion rate on stellar mass if the initial disk radius (before much viscous
evolution has occurred) has a strong dependence on stellar mass. However, it is
far from clear that at least the most massive pre-main sequence disks can be
totally magnetically activated by X-rays or cosmic rays. We suggest that a
combination of effects are responsible for the observed dependence, with the
lowest-mass stars having the lowest mass disks, which can be thoroughly
magnetically active, while the higher-mass stars have higher mass disks which
have layered accretion and relatively inactive or ``dead'' central zones at
some radii. In such dead zones, we suggest that gravitational instabilities may
play a role in allowing accretion to proceed. In this connection, we emphasize
the uncertainty in disk masses derived from dust emission, and argue that T
Tauri disk masses have been systematically underestimated by conventional
analyses. Further study of accretion rates, especially in the lowest-mass
stars, would help to clarify the mechanisms of accretion in T Tauri stars.
