Let P be any nonconstant complex polynomial and let \({\mathcal N}_ P\) denote the near-ring of all continuous selfmaps of the complex plane where addition of functions is pointwise and multiplication is defined by \(fg=f\circ P\circ g\) for all f,g\(\in {\mathcal N}_ P\). The near-ring \({\mathcal N}_ P\) is referred to as a laminated near-ring and P is the laminating element or laminator. In two previous papers, an investigation of the automorphism groups of such near-rings was initiated and in this one we complete the solution of the problem. Let GL(2) denote the full linear group of all real \(2\times 2\) nonsingular matrices, let \(G_ 1\) denote the subgroup of GL(2) consisting of those matrices where \(a_{11}=1\), \(a_{21}=0\) and \(a_{22}\neq 0\). Let \(G_ c\) denote the subgroup of GL(2) consisting of those matrices where \(a_{11}=a_{22}\), \(a_{12}=- a_{21}\) and \(a^ 2_{11}+a^ 2_{21}\neq 0\) and also those matrices where \(a_{11}=-a_{22}\), \(a_{21}=a_{12}\) and \(a^ 2_{11}+a^ 2_{21}\neq 0\). Finally, for each positive integer m, let \(GR_ m\) denote that subgroup of \(G_ c\) where \(a_{11}=\cos (2k\pi /m)\) and \(a_{21}=\sin (2k\pi /m)\), \(1\leq k\leq m\) and let \(Z_ m\) denote the cyclic group of order m. Then Aut \({\mathcal N}_ P\), the automorphism group of \({\mathcal N}_ P\), is isomorphic to one of the groups we have just described and the particular group to which Aut \({\mathcal N}_ P\) is isomorphic is determined by an inspection of the coefficients of P.