We study d=2+1 non-commutative U(1) YMCS, concentrating on the one-loop
corrections to the propagator and to the dispersion relations. Unlike its
commutative counterpart, this model presents divergences and hence an IR/UV
mechanism, which we regularize by adding a Majorana gaugino of mass m_f, that
provides (softly broken) supersymmetry. The perturbative vacuum becomes stable
for a wide range of coupling and mass values, and tachyonic modes are generated
only in two regions of the parameters space. One such region corresponds to
removing the supersymmetric regulator (m_f >> m_g), restoring the well-known
IR/UV mixing phenomenon. The other one (for m_f ~ m_g/2 and large \theta) is
novel and peculiar of this model. The two tachyonic regions turn out to be very
different in nature. We conclude with some remarks on the theory's off-shell
unitarity.Comment: 42 pages, 11 figures, uses Axodraw. Bibliography revise
