  We consider rotating magnetic stars with winds and disks. We establish a
theorem that relates the angular velocity of a disk region with no meridional
motion to the angular velocity of the star. Also, we show that for a given
value of the magnetic field strength, if the rotation rate is too high or the
flow velocity into the shock boundary is too low, a Keplerian disk region will
not be formed. We develop a model for the formation of disks in magnetic
rotators through the processes of fill-up and diffusion into Keplerian orbits.
At the end of the fill-up stage the density of the disk increases significantly
and the magnetic force in the disk becomes negligible. We derive analytical
expressions for the inner and outer radii of Keplerian disks in terms of the
stellar rotation rate. A disk can form if the meridional component Bm of the
field at the stellar surface is larger than a minimum value. The radial extent
of the Keplerian region becomes larger for larger values of Bm and is largest
when Bm equals an optimal value. The strengths of the minimum fields required
for Keplerian disk formation in B-type stars varies from order 1G to 10G. In
O-type stars they must be of order 500G. Also, we suggest that the stellar
magnetic fields may be affected by rotationally driven meridional circulation
leading to some of the the observed variations of disks with time.
