  Every complex plane curve C determines a subscheme S of the $P^8$ of 3x3
matrices, whose projective normal cone (PNC) captures subtle invariants of C.
In "Limits of PGL(3)-translates of plane curves, I" we obtain a set-theoretic
description of the PNC and thereby we determine all possible limits of families
of plane curves whose general element is isomorphic to C. The main result of
this article is the determination of the PNC as a cycle; this is an essential
ingredient in our computation in "Linear orbits of arbitrary plane curves" of
the degree of the PGL(3)-orbit closure of an arbitrary plane curve, an
invariant of natural enumerative significance.
