1998; Marconi & Hunt 2003; Haring & Rix 2004; Graham 2007) but, in particular, a tight correlation exists between the SMBH mass and the central projected stellar velocity dispersion $\sigma$ (Ferrarese & Merrit 2000; Gebhardt et al. 2000; Merrit & Ferrarese 2001; Tremaine et al. 2002). The mechanism (or mechanisms) responsible for establishing the M-$\sigma$ relation is (are) not yet well determined but several scenarios have been put forward in the past years to explain the origin of such a relation. Self-regulated growth of black holes by feedback effects produced either by outflows or UV-radiation from QSO’s, which affect also the star formation activity is a possible mechanism able to reproduce the M-$\sigma$ relation (Silk & Rees 1998; Sazonov et al. 2005). A relation between these physical quantities can also be obtained from the picture developed by Burkert & Silk (2001) in which black holes grow at the expense of a viscous accretion disk and whose gas reservoir beyond the BH influence radius feeds also the formation of stars.

These investigations seem to point to a well-defined road leading to the formation of SMBHs: the growth of ”seeds” by accretion inside the host galaxy. This picture is consistent with the 