  The spin is an important but poorly constrained parameter for describing
supermassive black holes (SMBHs). Using the continuity equation of SMBH number
density, we explicitly obtain the mass-dependent cosmological evolution of the
radiative efficiency for accretion, which serves as a proxy for SMBH spin. Our
calculations make use of the SMBH mass function of active and inactive galaxies
(derived in the first paper of this series), the bolometric luminosity function
of active galactic nuclei (AGNs), corrected for the contribution from
Compton-thick sources, and the observed Eddington ratio distribution. We find
that the radiative efficiency generally increases with increasing black hole
mass at high redshifts (z>~1), roughly as \eta \propto M_bh^0.5, while the
trend reverses at lower redshifts, such that the highest efficiencies are
attained by the lowest mass black holes. Black holes with M_bh>~10^8.5M_sun
maintain radiative efficiencies as high as \eta~0.3-0.4 at high redshifts, near
the maximum for rapidly spinning systems, but their efficiencies drop
dramatically (by an order of magnitude) by z~0. The pattern for lower mass
holes is somewhat more complicated but qualitatively similar. Assuming that the
standard accretion disk model applies, we suggest that the accretion history of
SMBHs and their accompanying 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; it occurs at z~2
for high-mass black holes, and somewhat later, at z~1, for lower-mass systems.
