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We derive the mass function of supermassive black holes (SMBHs) over theredshift range 0<z<2, using the latest deep luminosity and mass functions offield galaxies. Applying this mass function, combined with the bolometricluminosity function of active galactic nuclei (AGNs), into the the continuityequation of SMBH number density, we explicitly obtain the mass-dependentcosmological evolution of the radiative efficiency for accretion. We suggestthat the accretion history of SMBHs and their spins evolve in two distinctregimes: an early phase of prolonged accretion, plausibly driven by majormergers, during which the black hole spins up, then switching to a period ofrandom, episodic accretion, governed by minor mergers and internal secularprocesses, during which the hole spins down. The transition epoch depends onmass, mirroring other evidence for "cosmic downsizing" in the AGN population.

Cosmological Evolution of Supermassive Black Holes: Mass Functions and Spins