  The problem of the giant vortex state around a magnetic dot which is embedded
in a superconducting film is investigated. The full non-linear, self-consistent
Ginzburg-Landau equations are solved numerically in order to calculate the free
energy, the order parameter of the host superconductor, the internal magnetic
field due to the supercurrents, the corresponding current density, the
magnetization probed in the vicinity of the dot, and the normal electron
density as a function of the various parameters of the system. We find that, as
we increase the magnetic moment of the dot, higher flux quanta vortex states
become energetically more favorable, as they can better compete with the
external magnetic field via the Meissner effect. In addition to that, they
progressively become closer to each other in energy with direct experimental
consequences, i.e. physical quantities like magnetization may fluctuate when
measured, for example, as a function of a uniform external magnetic field.
