  The growth of supermassive black holes (BHs) located at the centers of their
host galaxies comes mainly from accretion of gas, but how to fuel them remains
an outstanding unsolved problem in quasar evolution. This issue can be
elucidated by quantifying the radiative efficiency parameter ($\eta$) as a
function of redshift, which also provides constraints on the average spin of
the BHs and its possible evolution with time. We derive a formalism to link
$\eta$ with the luminosity density, BH mass density, and duty cycle of quasars,
quantities we can estimate from existing quasar and galaxy survey data. We find
that $\eta$ has a strong cosmological evolution: at z~2, $\eta \approx 0.3$,
and by $z\approx 0$ it has decreased by an order of magnitude, to $\eta\approx
0.03$. We interpret this trend as evolution in BH spin, and we appeal to
episodic, random accretion as the mechanism for reducing the spin. The
observation that the fraction of radio-loud quasars decreases with increasing
redshift is inconsistent with the popular notion that BH spin is a critical
factor for generating strong radio jets. In agreement with previous studies, we
show that the derived history of BH accretion closely follows the cosmic
history of star formation, consistent with other evidence that BHs and their
host galaxies coevolve.
