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The normal matrix model with a cubic potential is ill-defined and it developsa critical behavior in finite time. We follow the approach of Bleher andKuijlaars to reformulate the model in terms of orthogonal polynomials withrespect to a Hermitian form. This reformulation was shown to capture theessential features of the normal matrix model in the subcritical regime, namelythat the zeros of the polynomials tend to a number of segments (the motherbody)inside a domain (the droplet) that attracts the eigenvalues in the normalmatrix model.  In the present paper we analyze the supercritical regime and we find that thelarge $n$ behavior is described by the evolution of a spectral curve satisfyingthe Boutroux condition. The Boutroux condition determines a system of contours$\Sigma_1$, consisting of the motherbody and whiskers sticking out of thedomain. We find a second critical behavior at which the original motherbodyshrinks to a point at the origin and only the whiskers remain.  In the regime before the second criticality we also give strong asymptoticsof the orthogonal polynomials by means of a steepest descent analysis of a $3\times 3$ matrix valued Riemann-Hilbert problem. It follows that the zeros ofthe orthogonal polynomials tend to $\Sigma_1$, with the exception of at mostthree spurious zeros.

The supercritical regime in the normal matrix model with cubic potential