  We study the effect of a Chern-Simons term on the electrically charged and
spinning solitons of several $U(1)$ gauged models in $2+1$ dimensions. These
are vortices of complex scalar field theories, both with and without symmetry
breaking dynamics, and the $O(3)$ Skyrme model. In all cases the gauge
decoupling limits are also considered. It is well known that the effect of the
Chern-Simons dynamics is to endow vortices with electric charge $Q_e$ and spin
$J$, but our main aim here is to reveal a new feature: that the mass-energy $E$
of the electrically charged vortex can be lower than that of the electrically
neutral one, in contrast to the usual monotonic increase of $E$ with $Q_e$.
These effects of Chern-Simons dynamics were observed previously in $3+1$
dimensional systems, and the present results can be viewed as corroborating the
latter. Moreover, the usual energy-spin relationship is likewise altered. We
carry out a detailed quantitative analysis of azimuthally symmetric vortices
and describe their qualitative features by constructing the solutions
numerically.
