  Quasars represent the brightest Active Galactic Nuclei (AGN) in the Universe
and 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 though
that such an extremely energetic process will take place in the most massive
bound structures in the dark matter (DM) distribution. We show that in contrast
to this expectation, in a galaxy formation model which includes AGN feedback,
quasars are predicted to live in average DM halo environments with typical
masses of a few times 10^12 Msun. This fundamental prediction arises from the
fact that quasar activity (i.e., BH accretion with luminosity greater than
10^46 erg/sec) is inhibited in DM haloes where AGN feedback operates. The
galaxy hosts of quasars in our simulations are identified with over massive (in
gas and stars) spheroidal galaxies, in which BH accretion is triggered via a
galaxy merger or secular processes. We further show that the z=0 descendants of
high redshift (z~6) QSOs span a wide range of morphologies, galaxy and halo
masses. 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 time
and 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 in
the abundance of galaxies around quasars at z~5. However, these enhancements
are considerably weaker compared to the overdensities expected at the extreme
peaks of the DM distribution. Thus, it is very unlikely that a quasar detected
in the $z\gtrsim5$ Universe pinpoints the location of the progenitors of
superclusters in the local Universe.
