  We investigate stationary models of magnetized, self-gravitating disks around
black holes. The disks are assumed to rotate according to a recently introduced
Keplerian rotation law. We consider different prescriptions of the toroidal
magnetic field. Similarly to the purely hydrodynamical case (i.e., with no
magnetic field), we observe a bifurcation in the parameter space of solutions.
There are usually two branches of solutions: a branch corresponding to
relatively light disks and a branch for which the disk can be more massive than
the black hole. The existence of this latter branch can be explained by
geometric properties of the spacetime. We investigate the influence of the
magnetic field in the disk on these effects.
