Plane curves with small linear orbits II

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 dimen sional stabilizer, and we compute the degree of the closure of the linear o rbits of curves supported on unions of lines. Together with the results of [3], this encompasses the enumerative geometry of all plane curves with sma ll linear orbit. This information will serve elsewhere as an ingredient in the computation of the degree of the orbit closure of an arbitrary plane cu rve.