  Using a combination of the variation approximation (VA) and direct
simulations, we consider the light transmission in nonlinearly amplified bulk
media, taking into account the localization of the gain, i.e., the linear loss
shaped as a parabolic function of the transverse radius, with a minimum at the
center. The balance of the transverse diffraction, self-focusing, gain, and the
inhomogeneous loss provide for the hitherto elusive stabilization of vortex
solitons in a large zone of the parameter space. Adjacent to it, stability
domains are found for several novel kinds of localized vortices, including
spinning elliptically shaped ones, eccentric elliptic vortices which feature
double rotation, spinning crescents, and breathing vortices.
