  We study some properties of topological Chern-Simons vortices in 2 + 1
dimensions. As has already been understood in the past, in the large magnetic
flux limit, they are well described by a Chern-Simons domain wall, which has
been compactified on a circle with the symmetric phase inside and the
asymmetric phase on the outside. Our goal is two-fold. First we want to explore
how the tension depends on the magnetic flux discretized by the integer n. The
BPS case is already known, but not much has been explored about the non-BPS
potentials. A generic renormalizable potential has two dimensionless parameters
that can be varied. Variation of only one of them lead to a type I and type II
vortex, very similar to the Abrikosov-Nielsen-Olesen (ANO) case. Variation of
both the parameters leads to a much richer structure. In particular we have
found a new type of vortex, which is type I-like for small flux and then turns
type II-like for larger flux. We could tentatively denote it a type III vortex.
This results in a stable vortex with number of fluxes which can be greater than
one. Our second objective is to study the Maxwell-Chern-Simons theory and and
understand how the large n limit of the CS vortex is smoothly connected with
the large n limit of the ANO vortex.
