  We present an extended study of anyonic Luttinger liquids wires jointing at a
single point. The model on the full line is solved with bosonization and the
junction of an arbitrary number of wires is treated imposing boundary
conditions that preserve exact solvability in the bosonic language. This allows
to reach, in the low momentum regime, some of the critical fixed points found
with the electronic boundary conditions. The stability of all the fixed points
is discussed.
