In this paper, inspired by the holographic dual of the entanglement entropy, we consider the behavior of extremal, codimension two, spacelike surfaces in the background of three and four dimensional charged boson stars in asymptotically anti-de Sitter spacetime. We find conditions for which families of minimal area surfaces fail to contain the entire bulk spacetime and construct a phase diagram showcasing the transition between regimes. In addition, we use the relation between the star's mass and the central density of the scalar field to argue for a possible instability of such hollow solutions. Finally, we discuss the consequences of our findings for the study of holographic duals of reduced density matrices.
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