Cosmological Evolution of Supermassive Black Holes: Mass Functions and
  Spins
  We derive the mass function of supermassive black holes (SMBHs) over the
redshift range 0<z<2, using the latest deep luminosity and mass functions of
field galaxies. Applying this mass function, combined with the bolometric
luminosity function of active galactic nuclei (AGNs), into the the continuity
equation of SMBH number density, we explicitly obtain the mass-dependent
cosmological evolution of the radiative efficiency for accretion. We suggest
that the accretion history of SMBHs and their spins evolve in two distinct
regimes: an early phase of prolonged accretion, plausibly driven by major
mergers, during which the black hole spins up, then switching to a period of
random, episodic accretion, governed by minor mergers and internal secular
processes, during which the hole spins down. The transition epoch depends on
mass, mirroring other evidence for "cosmic downsizing" in the AGN population.
