  Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we
study equilibrium and nonequilibrium phase transitions between different
superconducting states of mesoscopic disks which are thinner than the coherence
length and the penetration depth. We have found a smooth transition from a
multi-vortex superconducting state to a giant vortex state with increasing both
the disk thickness and the magnetic field. A vortex phase diagram is obtained
which shows, as function of the magnetic field, a re-entrant behavior between
the multi-vortex and the giant vortex state.
