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. 
Yan-Rong Li, Jian-Min Wang, Luis C. Ho
astro-ph.CO