  The growth of supermassive black holes by merging and accretion in
hierarchical models of galaxy formation is studied by means of Monte Carlo
simulations. A tight linear relation between masses of black holes and masses
of bulges arises if if the mass accreted by supermassive black holes scales
linearly with the mass forming stars and if the redshift evolution of mass
accretion tracks closely that of star formation. Differences in redshift
evolution between black hole accretion and star formation introduce
considerable scatter in this relation. A non-linear relation between black hole
accretion and star formation results in a non-linear relation between masses of
remnant black holes and masses of bulges. The relation of black hole mass to
bulge luminosity obseved in nearby galaxies and its scatter are reproduced
reasonably well by models in which black hole accretion and star formation are
linearly related but do not track each other in redshift. This suggests that a
common mechanism determines the efficiency for black hole accretion and the
efficiency for star formation, especially for bright bulges.
