  The vortex states in a thin mesoscopic disk are investigated within the
phenomenological Ginzburg-Landau theory in the presence of different ''model''
magnetic field profiles with zero average field which may result from a
ferromagnetic disk or circulating currents in a loop near the superconductor.
We calculated the dependences of both the ground and metastable states on the
magnitude and shape of the magnetic field profile for different values of the
order parameter angular moment, i.e. the vorticity. The regions of existence of
the multi-vortex state and the giant vortex state are found. We analysed the
phase transitions between these states and studied the contribution from
ring-shaped vortices. A new transition between different multi-vortex
configurations as the ground state is found. Furthermore, we found a vortex
state consisting of a central giant vortex surrounded by a collection of
anti-vortices which are located in a ring around this giant vortex. The limit
to a disk with an infinite radius, i.e. a film, will also be discussed. We also
extended our results to ''real'' magnetic field profiles and to the case in
which an external homogeneous magnetic field is present.
