The magnetization ground states (MGSs) for a nanosized Co hollow sphere, with the outer radius, R < 50 nm, have been studied numerically by micromagnetic simulation using object oriented micromagnetic framework (OOMMF). In addition to the originally known single domain and vortex-curling states, a three dimensional "onion" state with a corresponding analytical expression is proposed and confirmed as one of the ground states. Two phase diagrams, one for a single crystalline and the other for a

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... lycrystalline nanosphere, are obtained for the three MGSs. The result reveals that the magnetic anisotropy has a significant effect on the phase line in the diagrams. The finite temperature effect and the blocking properties of the nanosphere for the magnetization reversal are discussed.