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Quasars represent the brightest Active Galactic Nuclei (AGN) in the Universeand are thought to indicate the location of prodigiously growing Black Holes(BHs), with luminosities as high as 10^48 erg/sec. It is often expected thoughthat such an extremely energetic process will take place in the most massivebound structures in the dark matter (DM) distribution. We show that in contrastto this expectation, in a galaxy formation model which includes AGN feedback,quasars are predicted to live in average DM halo environments with typicalmasses of a few times 10^12 Msun. This fundamental prediction arises from thefact that quasar activity (i.e., BH accretion with luminosity greater than10^46 erg/sec) is inhibited in DM haloes where AGN feedback operates. Thegalaxy hosts of quasars in our simulations are identified with over massive (ingas and stars) spheroidal galaxies, in which BH accretion is triggered via agalaxy merger or secular processes. We further show that the z=0 descendants ofhigh redshift (z~6) QSOs span a wide range of morphologies, galaxy and halomasses. The z~6 BHs typically grow only by a modest factor by the present day.Remarkably, high redshift QSOs never inhabit the largest DM haloes at that timeand their descendants are very seldom found in the most massive haloes at z=0.We also show that observationally it is very likely to find an enhancement inthe abundance of galaxies around quasars at z~5. However, these enhancementsare considerably weaker compared to the overdensities expected at the extremepeaks of the DM distribution. Thus, it is very unlikely that a quasar detectedin the $z\gtrsim5$ Universe pinpoints the location of the progenitors ofsuperclusters in the local Universe.

The most luminous quasars do not live in the most massive dark matter haloes at any redshift