The Cosmological History of Accretion onto Supermassive Black Holes
  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. 
L. Miller, W.J. Percival, S.M. Croom