  A numerical model of a steady state, thin accretion disk with a constant
effective speed of sound is presented. We demonstrate that `zero torque' inner
boundary condition is a reasonable approximation provided that the disk
thickness, including the thickness of the torquing magnetic fields, is small
everywhere. It is likely that this conclusion is correct also for non-steady
disks, as long as the total thickness at the sonic point, H_c, is much smaller
than the radius there, r_c ~ r_{ms}. The very existence of thin disks is not
proved or disproved in this work, but such disks are believed to exist for
moderate accretion rates.
  Within our model there is a small torque at r_{ms}, which may increase disk
luminosity by several percent. An important result of our analysis is that the
physically acceptable steady state solutions in our toy model exist only for
\alpha < 0.14 (100 v_s/c)^{1/3}.
  A significant torque may be applied to a thin disk if there is a large scale
magnetic field, like in a modified Blandford-Znajek mechanism.
