decrease of the effectiveness of interactions in destabilizing the cold gas (see eq. 1 and the discussion in Menci et al. 2003).

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[ Fig. 2. - The QSO B-band luminosity functions from our model (solid lines) are shown for $z=0.55$ (lower curve), $z=1.2$ (middle curve) and $z=2.2$ (uppermost curve), and are compared with the data. These are taken from Hartwick & Shade (1990, solid squares) and Boyle et al. (2000, crosses), and rescaled to our cosmology with $\Omega_0=0.3$, $\Omega_{\lambda}=0.7$, $h=0.7$. We also show the model results for $z=3$ (dashed line) and $z=4$ (dotted line), compared to the Sloan data at $z04.2$ from Fan et al. (2001, diamonds). The blue luminosity $L_B$ has been obtained by applying a bolometric correction of 13 (Elvis et al. 1994) to the bolometric luminosity in eq. (3). ]{}

As a final test, we also probe the model predictions for the hot gas phase which is enriched by the gas expelled from the galaxies by the AGN feedback (see sect. 2.2). In particular we show in fig. 3 how the baryon fraction and the mass temperature relation resulting from the model compares with present observations. This shows that: i) that the amount of hot gas 