Multi-bar K configurations and the limit of kaon condensation

Our recent relativistic mean-field (RMF) calculations of multi?-? $bar K$ nuclei are briefly reviewed. I discuss the saturation pattern of the $bar K$ separation energy $B_{bar K}$ and nuclear densities on increasing the number of antikaons embedded in the nuclear medium. Saturation appears to be a robust feature of multi- $bar K$ nuclei. Because $B_{bar K}$ generally does not exceed 200 MeV, it is unlikely that kaon condensation occurs in strong-interaction self-bound strange hadronic matter. Last, I present our calculations of self-bound strange systems made out of neutrons and ${bar K}^0$ mesons.