  Direct and indirect observational evidence leads to the conclusion that high
redshift QSOs did shine in the core of early type proto-galaxies during their
main episode of star formation. Exploting this fact, we derive the rate of
formation of this kind of stellar systems at high redshift by using the QSO
Luminosity Function. The elemental proportions in elliptical galaxies, the
descendents of the QSO hosts, suggest that the star formation was more rapid in
more massive objects. We show that this is expected to occur in Dark Matter
haloes, when the processes of cooling and heating is considered. This is also
confirmed by comparing the observed sub-mm counts to those derived by coupling
the formation rate and the star formation rate of the spheroidal galaxies with
a detailed model for their SED evolution. In this scenario SCUBA galaxies and
Lyman Break Galaxies are early type proto-galaxies forming the bulk of their
stars before the onset of QSO activity.
