  We examine the effect of self-gravity in a rotating thick-disk equilibrium in
the presence of a dipolar magnetic field. In the first part, we find a
self-similar solution for non-self-gravitating disks. The solution that we have
found shows that the pressure and density equilibrium profiles are strongly
modified by a self-consistent toroidal magnetic field. We introduce 3
dimensionless variables $C_B$, $C_c$, $C_t$ that indicate the relative
importance of toroidal component of magnetic field ($C_B$), centrifugal ($C_c$)
and thermal ($C_t$) energy with respect to the gravitational potential energy
of the central object. We study the effect of each of them on the structure of
the disk. In the second part, we investigate the effect of self-gravity on the
these disks; thus we introduce another dimensionless variable ($C_g$) that
shows the importance of self-gravity. We find a self-similar solution for the
equations of the system. Our solution shows that the structure of the disk is
modified by the self-gravitation of the disk, the magnetic field of the central
object, and the azimuthal velocity of the gas disk. We find that self-gravity
and magnetism from the central object can change the thickness and the shape of
the disk. We show that as the effect of self-gravity increases the disk becomes
thinner. We also show that for different values of the star's magnetic field
and of the disk's azimuthal velocity, the disk's shape and its density and
pressure profiles are strongly modified.
