  We consider the shape of an accretion disc whose outer regions are misaligned
with the spin axis of a central black hole and calculate the steady state form
of the warped disc in the case where the viscosity and surface densities are
power laws in the distance from the central black hole. We discuss the shape of
the resulting disc in both the frame of the black hole and that of the outer
disc. We note that some parts of the disc and also any companion star maybe
shadowed from the central regions by the warp. We compute the torque on the
black hole caused by the Lense-Thirring precession and hence compute the
alignment and precession timescales. We generalise the case with viscosity and
hence surface density independent of radius to more realistic density
distributions for which the surface density is a decreasing function of radius.
We find that the alignment timescale does not change greatly but the precession
timescale is more sensitive. We also determine the effect on this timescale if
we truncate the disc. For a given truncation radius, the the timescales are
less affected for more sharply falling density distributions.
