  We use three dimensional magnetohydrodynamic simulations, in a
pseudo-Newtonian potential, to study geometrically thin accretion disc flows
crossing the marginally stable circular orbit around black holes. We
concentrate on vertically unstratified and isothermal disk models, but also
consider a model that includes stratification. In all cases, we find that the
sonic point lies just inside the last stable orbit, with a modest increase in
the importance of magnetic field energy, relative to the thermal energy,
observed interior to this radius. The time-averaged gradient of the specific
angular momentum of the flow, (dl/dr), is close to zero within the marginally
stable orbit, despite the presence of large fluctuations and continuing
magnetic stress in the plunging region. The result that the specific angular
momentum is constant within the last stable orbit is in general agreement with
traditional disk models computed using a zero-torque boundary condition at the
last stable orbit.
