  Using multiwavelength surveys of active galactic nuclei across a wide range
of bolometric luminosities (10^{43}<L_{bol}(erg/s<5x10^{46}) and redshifts
(0<z<3), we find a strong, redshift-independent correlation between the AGN
luminosity and the fraction of host galaxies undergoing a major merger. That
is, only the most luminous AGN phases are connected to major mergers, while
less luminous AGN appear to be driven by secular processes. Combining this
trend with AGN luminosity functions to assess the overall cosmic growth of
black holes, we find that ~50% by mass is associated with major mergers, while
only 10% of AGN by number, the most luminous, are connected to these violent
events. Our results suggest that to reach the highest AGN luminosities -where
the most massive black holes accreted the bulk of their mass - a major merger
appears to be required. The luminosity dependence of the fraction of AGN
triggered by major mergers can successfully explain why the observed scatter in
the M-\sigma relation for elliptical galaxies is significantly lower than in
spirals. The lack of a significant redshift dependence of the
L_{bol}-f_{merger} relation suggests that downsizing, i.e., the general decline
in AGN and star formation activity with decreasing redshift, is driven by a
decline in the frequency of major mergers combined with a decrease in the
availability of gas at lower redshifts.
