of the SMBHs in the host galaxy.

On the thoretical side, the impact of AGN feedback on galaxy formation has been investigated in a number of papers (Murray, Quataert & Thompson, Monaco & Fontanot 2005, Begelman & Nath 2005; Scannapieco, Silk & Bowens 2005); all the different assumed mechanisms for the energy injection can produce the expulsion of a significant fraction of the interstellar gas; the effectiveness of the AGN feedback in quenching the black hole growth and the subsequent star formation has been confirmed by recent aimed simulations of galaxy collisions triggering AGN activity (Di Matteo , Springel & Hernquist 2005) and of AGN feeding activated by gas infall (Kawata & Gibson 2005). However, inserting such a mechanism into a cosmological framework of galaxy formation constitues a challenging task. The model by Granato et al. (2004) successfully uses the shining of QSOs as a clock for the formation of elliptical galaxies, but does not include spiral galaxies, nor it provides predictions for the lower- energy AGNs at $z<1$. In ”ab initio” hierarchical models of galaxy formation in a cosmolgical context (Bower et al. 2005, Cattaneo et al. 2006; Croton et al. 2006; Kang, Jing, Silk 2006) SMBHs are assumed 