Under the combined effect of accretion and the Blandford-Znajek process, th
e dimensionless angular momentum of the central black hole in AGNe grows to
a stable value below that for the extreme Kerr black hale, so the third la
w of black hole thermodynamics is not violated. The stable value exists-for
both thin and thick disks; its size is determined by the strength of the B
-Z process and the disk geometry and is independent of the black hole mass
or the accretion rate.