  We incorporate a simple scheme for the growth of supermassive black holes
into semi-analytic models that follow the formation and evolution of galaxies
in a cold dark matter dominated Universe. We assume that supermassive black
holes are formed and fuelled during major mergers. If two galaxies of
comparable mass merge, their central black holes coalesce and a few percent of
the gas in the merger remnant is accreted by the new black hole over a
timescale of a few times 10^7 years. With these simple assumptions, our model
not only fits many aspects of the observed evolution of galaxies, but also
reproduces quantitatively the observed relation between bulge luminosity and
black hole mass in nearby galaxies, the strong evolution of the quasar
population with redshift and the relation between the luminosities of nearby
quasars and those of their host galaxies. The strong decline in the number
density of quasars from z=2 to z=0 is due to the combination of three effects:
i) a decrease in the merging rate, ii) a decrease in the amount of cold gas
available to fuel black holes, and iii) an increase in the timescale for gas
accretion. In a LCDM cosmology the predicted decline in the total content of
cold gas in galaxies is consistent with that inferred from observations of
damped Lyman-alpha systems. Our results strongly suggest that the evolution of
supermassive black holes, quasars and starbursts is inextricably linked to the
hierarchical build-up of galaxies.
