We explore the connection between black hole growth at the center of obscured quasars selected from the XMM-COSMOS survey and the physical properties of their host galaxies. We study a bolometric regime (<Lbol > 8 x 10^45 erg/s) where several theoretical models invoke major galaxy mergers as the main fueling channel for black hole accretion. We confirm that obscured quasars mainly reside in massive galaxies (Mstar>10^10 Msun) and that the fraction of galaxies hosting such powerful quasars monotonically increases with the stellar mass. We stress the limitation of the use of rest-frame color-magnitude diagrams as a diagnostic tool for studying galaxy evolution and inferring the influence that AGN activity can have on such a process. We instead use the correlation between star-formation rate and stellar mass found for star-forming galaxies to discuss the physical properties of the hosts. We find that at z ~1, ~62% of Type-2 QSOs hosts are actively forming stars and that their rates are comparable to those measured for normal star-forming galaxies. The fraction of star-forming hosts increases with redshift: ~71% at z ~2, and 100% at z ~3. We also find that the the evolution from z ~1 to z ~3 of the specific star-formation rate of the Type-2 QSO hosts is in excellent agreement with that measured for star-forming galaxies. From the morphological analysis, we conclude that most of the objects are bulge-dominated galaxies, and that only a few of them exhibit signs of recent mergers or disks. Finally, bulge-dominated galaxies tend to host Type-2 QSOs with low Eddington ratios (lambda<0.1), while disk-dominated or merging galaxies have at their centers BHs accreting at high Eddington ratios (lambda > 0.1).
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