  In this work we present some new results obtained in a study of the phase
diagram of charged compact boson stars in a theory involving a complex scalar
field with a conical potential coupled to a U(1) gauge field and gravity. We
here obtain new bifurcation points in this model. We present a detailed
discussion of the various regions of the phase diagram with respect to the
bifurcation points. The theory is seen to contain rich physics in a particular
domain of the phase diagram.
