  In this paper we report on the formation of magnetically-levitating accretion
disks around supermassive black holes. The structure of these disks is
calculated by numerically modelling tidal disruption of magnetized interstellar
gas clouds. We find that the resulting disks are entirely supported by the
pressure of the magnetic fields against the component of gravitational force
directed perpendicular to the disks. The magnetic field shows ordered
large-scale geometry that remains stable for the duration of our numerical
experiments extending over 10% of the disk lifetime. Strong magnetic pressure
allows high accretion rate and inhibits disk fragmentation. This in combination
with the repeated feeding of manetized molecular clouds to a supermassive black
hole yields a possible solution to the long-standing puzzle of black hole
growth in the centres of galaxies.
