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 of realizing giant vortex states and states with nonuniform 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 nonuniform vorticity into a vortex lattice, when the magnetic field is adapted so that a phase boundary is crossed.