  We predict polarimetric line profiles for scattering off rotating disks using
a Monte Carlo technique. We have discovered that there is a marked difference
between scattering of line emission by a disk that reaches the stellar surface,
and a disk with an inner hole. For the case with an inner hole, we find single
position-angle rotations, similar to those predicted by analytic models. For
the case of an undisrupted disk, we find double rotations in the position angle
-- an effect not reported before. We show that this new effect is due to the
finite-sized star interacting with the disk's rotational velocity field. Since
a gradual increase of the hole size transforms the double rotations smoothly
back into single ones -- as the line emission object approaches that of a point
source -- our models demonstrate the diagnostic potential of line polarimetry
in determining not only the disk inclination, but also the size of the disk
inner hole. Our models are generic, and relevant to any line emitting object
that is embedded in a rotating disk. Examples are: Herbig Ae stars, T Tauri
stars, other young stars, early-type stars with disks, post-AGB stars,
cataclysmic variables and other binary systems, as well as extra-galactic
objects, such as the disks around super-massive black holes.
