  We present the results of axisymmetric, time-dependent magnetohydrodynamic
simulations of accretion flows around black holes. The calculations begin from
a rotationally supported thick torus which contains a weak poloidal field.
Accretion is produced by growth and saturation of the magnetorotational
instability (MRI) provided the wavelength of the fastest growing mode is less
than the thickness of the torus. Using a computational grid that spans more
than two decades in radius, we compare the time-averaged properties of the flow
to previous hydrodynamical simulations. The net mass accretion rate is small
compared to the mass inflow and outflow rates at large radii associated with
turbulent eddies. Turbulence is driven by the MRI rather than convection. The
two-dimensional structure of the time-averaged flow is significantly different
compared to the hydrodynamical case. We discuss the limitations imposed on our
results by the assumption of axisymmetry and the relatively small radial
domain.
