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.
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