  We derive quantitative predictions of the optical and X-ray luminosity
functions (LF) for QSs in the redshift range $z<3$. Based on BH paradigm, we
investigate how the accretion is controlled by the surrounding structures, as
these grow hierarchically. We argue that for $z < 3$ efficient black hole
fueling is triggered by the encounters of a gas-rich host with its companions
in a group. The dispersion of the dynamical parameters in the encounters
produces a double power-law LF. Strong luminosity evolution (LE) is produced as
these encounters deplete the gas supply in the host; an additional, milder
density evolution obtains since the interactions become progressively rarer as
the groups grow richer but less dense. From the agreement with the optical and
the X-ray data, we conclude that the evolution of the bright quasars is
articulated in two ways. Earlier than $z~3$ the gas-rich protogalaxies grow by
merging, which also induces parallel growth of central holes accreting at
Eddington rates. In the later era of group assemblage the host encounters with
companions drive onto already existing holes further but meager accretion;
these consume the gas in the hosts, and cause supply-limited emissions which
are intermittent, go progressively sub-Eddington and peter out. Then other
fueling processes come to the foreground; we discuss the faint emissions,
especially noticeable in X-rays, which are expected when hosts in the field
cannibalize satellite galaxies with their meager gas contents.
