  It is argued that supermassive black holes in the nuclei of galaxies most
likely have grown coevally with their host dark matter halos. A calculation
based on Press-Schechter within this framework shows that the mean rate of
accretion of matter onto such black holes varies from a value about 0.003 of
the Eddington rate at the present epoch to a value around 0.08 at redshift 3.
The bulk of AGN evolution may be explained as a reflection of the diminishing
rate of accretion of material onto galaxies. The result is almost independent
of mass of host dark matter halo and is only weakly dependent on the values of
cosmological parameters. At high redshifts, z greater than about 5, black holes
in galaxies would have been accreting close to the Eddington limit, which is
likely to lead to galactic outflows being ubiquitous at those epochs.
