  We find solutions of a gravity-Yang-Mills-Higgs theory in four dimensions
that represent asymptotic anti-de Sitter charged black holes with partial/full
gauge symmetry breaking. We then apply the AdS/CFT correspondence to study the
strong coupling regime of a $2+1$ quantum field theory at temperature $T$ and
finite chemical potential, which undergoes transitions to phases exhibiting the
condensation of a composite charged vector operator below a critical
temperature $T_c$, presumably describing $p+ip/p$-wave superconductors. In the
case of $p+ip$-wave superconductors the transitions are always of second order.
But for $p$-wave superconductors we determine the existence of a critical value
$\alpha_c$ of the gravitational coupling (for fixed Higgs v.e.v. parameter
$\hat m_W$) beyond which the transitions become of first order. As a
by-product, we show that the $p$-wave phase is energetically favored over the
$p+ip$ one, for any values of the parameters. We also find the ground state
solutions corresponding to zero temperature. Such states are described by
domain wall geometries that interpolate between $AdS_4$ spaces with different
light velocities, and for a given $\hat m_{W}$, they exist below a critical
value of the coupling. The behavior of the order parameter as function of the
gravitational coupling near the critical coupling suggests the presence of
second order quantum phase transitions. We finally study the dependence of the
solution on the Higgs coupling, and find the existence of a critical value
beyond which no condensed solution is present.
