  We study relativistic massive vector condensation due to a non zero chemical
potential associated to some of the global conserved charges of the theory. We
show that the phase structure is very rich. More specifically there are three
distinct phases depending on the value of one of the zero chemical potential
vector self interaction terms. We also develop a formalism which enables us to
investigate the vacuum structure and dispersion relations in the spontaneously
broken phase of the theory. We show that in a certain limit of the couplings
and for large chemical potential the theory is not stable. This limit,
interestingly, corresponds to a gauge type limit often employed to economically
describe the ordinary vector mesons self interactions in QCD. We finally
indicate for which physical systems our analysis is relevant.
