  Within the non-linear Ginzburg-Landau (GL) theory, we investigate the vortex
structure in a superconducting thin film with a ferromagnetic disk on top of
it. Antivortices are stabilized in shells around a central core of vortices (or
a giant-vortex) with size-magnetization controlled ``magic numbers''. An
equilibrium vortex phase diagram is constructed. The transition between the
different vortex phases occurs through the creation of a vortex-antivortex pair
under the magnetic disk edge.
