  We study junctions of single-channel spinless Luttinger liquids using
bosonisation. We generalize earlier studies by allowing the junction to be
superconducting and find new charge non-conserving low energy fixed points. We
establish the existence of $g \leftrightarrow 1/g$ duality (where $g$ is the
Luttinger Liquid parameter) between the charge conserving (normal) junction and
the charge non-conserving (superconducting) junction by evaluating and
comparing the scaling dimensions of various operators around the fixed points
in normal and superconducting sectors of the theory. For the most general
two-wire junction, we show that there are two conformally invariant
one-parameter families of fixed points which are also connected by a duality
transformation. We also show that the stable fixed point for the two-wire
superconducting junction corresponds to the situation where the crossed Andreev
reflection is perfect between the wires. For the three-wire junction, we study,
in particular, the superconducting analogs of the chiral, $D_P$ and the
disconnected fixed points obtained earlier in the literature in the context of
charge conserving three-wire junctions. We show that these fixed points can be
stabilized for $g < 1$ (repulsive electrons) within the superconducting sector
of the theory which makes them experimentally relevant.
