  We continue the investigation of supersymmetric extensions of baby Skyrme
models in d=2+1 dimensions. In a first step, we show that the CP(1) form of the
baby Skyrme model allows for the same N=1 SUSY extension as its O(3)
formulation. Then we construct the N=1 SUSY extension of the gauged baby Skyrme
model, i.e., the baby Skyrme model coupled to Maxwell electrodynamics. In a
next step, we investigate the issue of N=2 SUSY extensions of baby Skyrme
models. We find that all gauged and ungauged submodels of the baby Skyrme model
which support BPS soliton solutions allow for an N=2 extension such that the
BPS solutions are one-half BPS states (i.e., annihilated by one-half of the
SUSY charges). In the course of our investigation, we also derive the general
BPS equations for completely general N=2 supersymmetric field theories of (both
gauged and ungauged) chiral superfields, and apply them to the gauged nonlinear
sigma model as a further, concrete example.
