  The formation of $K^-$ and $\bar K^0$ condensation in $\beta$-equilibrated
hyperonic matter is investigated within a relativistic mean field model. In
this model, baryon-baryon and (anti)kaon-baryon interactions are mediated by
the exchange of mesons. It is found that antikaon condensation is not only
sensitive to the equation of state but also to antikaon optical potential
depth. For large values of antikaon optical potential depth, $K^-$ condensation
sets in before the appearance of negatively charged hyperons. We treat $K^-$
condensation as a first order phase transition. The Gibbs criteria and global
charge conservation laws are used to describe the mixed phase. Nucleons and
$\Lambda$ hyperons behave dynamically in the mixed phase. A second order phase
transition to $\bar K^0$ condensation occurs in the pure $K^-$ condensed phase.
Along with $K^-$ condensation, $\bar K^0$ condensation makes the equation of
state softer thus resulting in smaller maximum mass stars compared with the
case without any condensate. This equation of state also leads to a stable
sequence of compact stars called the third family branch, beyond the neutron
star branch. The compact stars in the third family branch have different
compositions and smaller radii than that of the neutron star branch.
