We will assume throughout this paper that polynomials are nonconstant. Let P be any complex polynomial and let p denote the near-ring of all continuous selfmaps of the complex plane where addition of functions is pointwise and multiplication is defined by fg = f ο P ο g for all f,g∈p. The near-ring p is referred to as a laminated near-ring and P is referred to as the laminating element or laminator. In [1] the problem was posed of determining Aut p the automorphism group of p. It was shown that exactly three infinite groups occur as automorphism groups of the laminated near-rings p and for each of the three groups those polynomials P were characterized such that Aut p is isomorphic to that particular group. The infinite groups turn out to be GL(2), the full linear group of all 2×2 nonsingular real matrices and two of its subgroups.