  The Bogomolnyi-Prasad-Sommerfield (BPS) baby Skyrme model coupled to gravity
is considered. We show that in an asymptotically flat space-time the model
still possesses the BPS property, i.e., admits a BPS reduction to first order
Bogomolnyi equations, which guarantees that the corresponding proper energy is
a linear function of the topological charge. We also find the mass-radius
relation as well as the maximal mass and radius. All these results are obtained
in an analytical manner, which implies the complete solvability of this
selfgravitating matter system. If a cosmological constant is added, then the
BPS property is lost. In de Sitter (dS) space-time both extremal and
non-extremal solutions are found, where the former correspond to finite
positive pressure solutions of the flat space-time model. For the asymptotic
anti-de Sitter (AdS) case, extremal solutions do not exist as there are no
negative pressure BPS baby Skyrmions in flat space-time. Non-extremal solutions
with AdS asymptotics do exist and may be constructed numerically. The impact of
the negative cosmological constant on the mass-radius relation is studied. We
also found two potentials for which exact multi-soliton solutions in the
external AdS space can be obtained. Finally, we elaborate on the implications
of these findings for certain three-dimensional models of holographic QCD.
