The aim of this thesis is to investigate the key points concerning the evolution of the local Super-massive Black Hole (SMBH) population and to understand the origin of the links the SMBH have with their host spheroidal galaxies and dark matter (DM) halos. In fact the tight correlations observed among the SMBH mass, the photometric and dynamical properties of the host galaxy and DM halo, suggest that these systems must have co-evolved during time building up together.
The study of the statistical mass distribution of the local SMBH population and galaxies and their link with the overall AGN statistics are fundamental tools to get important physical insights on the basic average features of SMBH evolution.
Any galaxy formation model must compare with such findings. For this purpose I have worked with the semi-analytical code developed by Granato et al. (2004) to physically model SMBH evolution in galaxies and DM halos, compare model results with empirical derivations and make predictions. In particular, my work has been primarily to tune the parameters and also try to arrange minor modifications, where needed, in order to cope with the variety of the numerous empirical data the model can successfully account for
