  We investigate the phase space of multi-centered near-extremal configurations
previously studied in arXiv:1108.5821 and arXiv:1110.5641 in the probe limit.
We confirm that in general the energetically favored ground state of the
multi-center potential, which can be a single or multi-center configuration,
has the most entropy and is thus thermodynamically stable. However, we find the
surprising result that for a subset of configurations, even though a single
center black hole seems to be energetically favored, it is entropically not
allowed (the resulting black hole would violate cosmic censorship). This
disproves classical intuition that everything would just fall into the black
hole if energetically favored. Along the way we highlight a shortcoming in the
literature regarding the computation of the angular momentum coming from
electromagnetic interaction in the probe limit and rectify it. We also
demonstrate that static supertubes can exist inside ergoregions where ordinary
point particles would be frame dragged.
