  In superconductors, the search for special vortex states such as giant
vortices focuses on laterally confined or nanopatterned thin superconducting
films, disks, rings, or polygons. We examine the possibility to realize giant
vortex states and states with non-uniform vorticity on a superconducting
spherical nanoshell, due to the interplay of the topology and the applied
magnetic field. We derive the phase diagram and identify where, as a function
of the applied magnetic field, the shell thickness and the shell radius, these
different vortex phases occur. Moreover, the curved geometry allows these
states (or a vortex lattice) to coexist with a Meissner state, on the same
curved film. We have examined the dynamics of the decay of giant vortices or
states with non-uniform vorticity into a vortex lattice, when the magnetic
field is adapted so that a phase boundary is crossed.
