  Several thin, Keplerian, sub-parsec megamaser disks have been discovered in
the nuclei of active galaxies and used to precisely determine the mass of their
host black holes. We show that there is an empirical linear correlation between
the disk radius and the black hole mass. We demonstrate that such disks are
naturally formed by the partial capture of molecular clouds passing through the
galactic nucleus and temporarily engulfing the central supermassive black hole.
Imperfect cancellation of the angular momenta of the cloud material colliding
after passing on opposite sides of the hole leads to the formation of a compact
disk. The radial extent of the disk is determined by the efficiency of this
process and the Bondi-Hoyle capture radius of the black hole, and naturally
produces the empirical linear correlation of the radial extent of the maser
distribution with black hole mass. The disk has sufficient column density to
allow X-ray irradiation from the central source to generate physical and
chemical conditions conducive to the formation of 22 GHz H2O masers. For
initial cloud column densities less than ~10^{23.5} cm^-2 the disk is non-self
gravitating, consistent with the ordered kinematics of the edge-on megamaser
disks; for higher cloud columns the disk would fragment and produce a compact
stellar disk similar to that observed around Sgr A* at the galactic centre.
