  We investigate the alignment processes of spinning black holes and their
surrounding warped accretion disks in a frame of two different types of feeding
at the outer boundaries. We consider (1) fixed flows in which gas is
continually fed with a preferred angular momentum, and (2) free flows in which
there is no gas supply and the disks diffuse freely at their outer edges. As
expected, we find that for the cases of fixed flows the black hole disk systems
always end up aligning on timescales of several 1e6 yr, irrespective of the
initial inclinations. If the initial inclination angles are larger than pi/2,
the black hole accretion transits from retrograde to prograde fashion, and the
accreted mass onto the black holes during these two phases is comparable. On
the other hand, for the cases of free flows, both alignments and
anti-alignments can occur, depending on the initial inclinations and the ratios
of the angular momentum of the disks to that of the black holes. In such cases,
the disks will be consumed within timescales of 1e6 yr by black holes accreting
at the Eddington limit. We propose that there is a close connection between the
black hole spin and the lifetime for which the feeding persists, which
determines the observable episodic lifetimes of active galactic nuclei. We
conclude that careful inclusion of the disk feeding at the outer boundaries is
crucial for modeling the evolution of the black hole spin.
