  The quantization of magnetic flux in superconductors is usually seen as
vortices penetrating the sample. While vortices are unstable in bulk type I
superconductors, restricting the superconductor causes a variety of vortex
structures to appear. We present a systematic study of giant vortex states in
type I superconductors obtained by numerically solving the Ginzburg-Landau
equations. The size of the vortices is seen to increase with decreasing film
thickness. In type I superconductors, giant vortices appear at intermediate
thicknesses but they do not form a well-defined vortex lattice. In the thinnest
type I films, singly quantized vortices seem to be stabilized by the geometry
of the sample instead of an increase in the effective Ginzburg-Landau
parameter.
