  We investigate how accretion episodes onto massive black holes power quasars
and AGN while they accumulate mass into the holes. We compute both the trend
and the stochastic component to the trigger of the accretion events, as
provided by structure buildup after the hierarchical paradigm. We base on host
galaxy evolution proceeding from the protogalactic era at redshifts z > 2.5
dominated by major merging events in high density regions, to the subsequent
era marked by galaxy-galaxy interactions in newly forming groups. These
dynamical events perturb the gravitational equilibrium of the gas reservoir in
the hosts, and trigger recurrent accretion episodes controlled by energy
feedback from the very source emission onto the surrounding gas. Depletion of
the latter by these events (adding to quiescent star formation) concurs with
the slowing down of the clustering to cause a fast drop of the activity in
dense regions. Meanwhile, in the "field" later and rarer events are triggered
by interactions of still gas-rich galaxies, and eventually by captures of dwarf
satellite galaxies; these are also included in our analytic model. Thus we
compute the quasar and AGN luminosity functions; we find these to brighten and
rise from z ~ 6 to z ~ 2.5, and then toward z ~ 0 to dim and fall somewhat, in
detailed agreement with the observations. We predict that for z < 2.5 the mass
distribution of the holes progressively rises and shifts rightwards; we compare
our results with the local data. We also find that downward of z ~ 2.5 the
Eddington ratios related to emitting, most massive holes drift below unity on
average, with a widening scatter; meanwhile, some smaller holes flare up closer
to the Eddington limit.
