  We investigate the relation between the BPS baby Skyrme model and its vector
meson formulation, where the baby Skyrme term is replaced by a coupling between
the topological current $B_\mu$ and the vector meson field $\omega_\mu$. The
vector model still possesses infinitely many symmetries leading to infinitely
many conserved currents which stand behind its solvability. It turns out that
the similarities and differences of the two models depend strongly on the
specific form of the potential. We find, for instance, that compactons (which
exist in the BPS baby Skyrme model) disappear from the spectrum of solutions of
the vector counterpart. Specifically, for the vector model with the old baby
Skyrme potential we find that it has compacton solutions only provided that a
delta function source term effectively screening the topological charge is
inserted at the compacton boundary. For the old baby Skyrme potential squared
we find that the vector model supports exponentially localized solitons, like
the BPS baby Skyrme model. These solitons, however, saturate a BPS bound which
is a nonlinear function of the topological charge and, as a consequence, higher
solitons are unstable w.r.t. decay into smaller ones, which is at variance with
the more conventional situation (a linear BPS bound and stable solitons) in the
BPS baby Skyrme model.
