The realignment of a black hole misaligned with its accretion disc

We calculate the rate at which a black hole aligns its angular momentum vector with that of matter accreting on to it through an accretion disc, in the approximation that the angle between the two angular momentum vectors is small. Much of the incoming misaligned angular momentum is transported outward by viscous couples (just as nearly all of the aligned angular momentum is transported outward in a flat accretion disc); nevertheless, the realignment rate is of the same order of magnitude as it would be if the angular momentum change at the radius of the warp were all taken up by the black hole.