  We have calculated the equilibrium properties of a star in a circular,
equatorial orbit about a Super-Massive Black Hole (SMBH), when the star fills
and overflows its Roche lobe. The mass transfer time scale is anticipated to be
long compared with the dynamical time and short compared with the thermal time
of the star, so that the entropy as a function of the interior mass is
conserved. We have studied how the stellar entropy, pressure, radius, mean
density, and orbital angular momentum vary when the star is evolved
adiabatically, for a representative set of stars. We have shown that the
stellar orbits change with the stellar mean density. Therefore, sun-like stars,
upper main sequence stars and red giants will spiral inward and then outward
with respect to the hole in this stable mass transfer process, while lower main
sequence stars, brown dwarfs and white dwarfs will always spiral outward.
