some simulated black holes is shown. It is possible to verify that there are periods during which the black hole mass remains constant (case of a ”dormant" black hole) and periods of gas accretion during which the black hole mass increases. In such a phase, the galaxy has an active nucleus, being associated to an AGN or to a QSO. Notice that only at $z \leq 4$ some black holes having masses greater than $10^7~M_\odot$ have appeared.

During the activity phase, the associated accretion disk is quite luminous and the luminosity depends essentially on the accretion rate. For a given redshift it is possible to compute the total luminosity due to all active black holes and, consequently, to estimate the comoving luminosity density. Such a luminosity density can be compared with observational data, permitting to test the robustness of the simulations. Figure 2 compares the luminosity density evolution derived from simulations with data by Hopkins et al. (2007). The agreement is quite satisfactory suggesting that the main physical aspects of the growth process are reasonably taken into account in the simulations.

Another successful comparison concerns the relation between the present SMBH mass with the central velocity dispersion of galaxies projected 