  The `linear orbit' of a plane curve of degree d is its orbit in P^{d(d+3)/2}
under the natural action of PGL(3). We classify curves with positive
dimensional stabilizer, and we compute the degree of the closure of the linear
orbits of curves supported on unions of lines. Together with the results of
math.AG/9805020, this encompasses the enumerative geometry of all plane curves
with small linear orbit. This information will serve elsewhere as an ingredient
in the computation of the degree of the orbit closure of an arbitrary plane
curve.
