  The normal matrix model with a cubic potential is ill-defined and it develops
a critical behavior in finite time. We follow the approach of Bleher and
Kuijlaars to reformulate the model in terms of orthogonal polynomials with
respect to a Hermitian form. This reformulation was shown to capture the
essential features of the normal matrix model in the subcritical regime, namely
that the zeros of the polynomials tend to a number of segments (the motherbody)
inside a domain (the droplet) that attracts the eigenvalues in the normal
matrix model.
  In the present paper we analyze the supercritical regime and we find that the
large $n$ behavior is described by the evolution of a spectral curve satisfying
the Boutroux condition. The Boutroux condition determines a system of contours
$\Sigma_1$, consisting of the motherbody and whiskers sticking out of the
domain. We find a second critical behavior at which the original motherbody
shrinks to a point at the origin and only the whiskers remain.
  In the regime before the second criticality we also give strong asymptotics
of 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 of
the orthogonal polynomials tend to $\Sigma_1$, with the exception of at most
three spurious zeros.
