The behavior of gravitational phase transitions in a system of concentric,
spherical, mass shells that interact via their mutual and self-gravitation
is investigated. The nature of the transition in the microcanonical,
canonical, and grand canonical ensembles is studied both theoretically in
terms of the mean-field limit and by dynamical simulation. Transitions
between a quasi-uniform state and a centrally concentrated state are
predicted by mean-field theory for the microcanonical and canonical
ensembles and this is supported by dynamical simulation. For the grand
canonical ensemble, mean-field theory predicts that no transition takes
place and that the thermodynamically stable state is always the uniform one.
Again, this result is supported by simulation under various initial mass distributions, even when the system is initialized in a collapsed state. In
addition to testing the predictions of the mean-field theory and studying
the effects of finite size scaling, dynamical simulation allows us to
examine the behavior of temporal and positional correlations that are
predicted to vanish in the mean-field limit.