  Warped accretion disks have attracted intensive attention because of their
critical role on shaping the spin of supermassive massive black holes (SMBHs)
through the Bardeen-Petterson effect, a general relativistic effect that leads
to final alignments or anti-alignments between black holes and warped accretion
disks. We study such alignment processes by explicitly taking into account the
finite sizes of accretion disks and the episodic lifetimes of AGNs that
delineate the duration of gas fueling onto accretion disks. We employ an
approximate global model to simulate the evolution of accretion disks, allowing
to determine the gravitomagnetic torque that drives the alignments in a quite
simple way. We then track down the evolutionary paths for mass and spin of
black holes both in a single activity episode and over a series of episodes.
Given with randomly and isotropically oriented gas fueling over episodes, we
calculate the spin evolution with different episodic lifetimes and find that it
is quite sensitive to the lifetimes. We therefore propose that spin
distribution of SMBHs can place constraints on the episodic lifetimes of AGNs
and vice versa. Applications of our results on the observed spin distributions
of SMBHs and the observed episodic lifetimes of AGNs are discussed, although
both the measurements at present are yet ambiguous to draw a firm conclusion.
Our prescription can be easily incorporated into semi-analytic models for black
hole growth and spin evolution.
