  We consider the orthogonal polynomials $\{P_{n}(z)\}$ with respect to the
measure $|z-a|^{2N c} {\rm e}^{-N |z|^2} \,{\rm d} A(z)$ over the whole complex
plane. We obtain the strong asymptotic of the orthogonal polynomials in the
complex plane and the location of their zeros in a scaling limit where $n$
grows to infinity with $N$.
  The asymptotics are described in terms of three (probability) measures
associated with the problem. The first measure is the limit of the counting
measure of zeros of the polynomials, which is captured by the $g$-function much
in the spirit of ordinary orthogonal polynomials on the real line. The second
measure is the equilibrium measure that minimizes a certain logarithmic
potential energy, supported on a region $K$ of the complex plane. The third
measure is the harmonic measure of $K^c$ with a pole at $\infty$. This appears
as the limit of the probability measure given (up to the normalization
constant) by the squared modulus of the $n$-th orthogonal polynomial times the
orthogonality measure, i.e. $|P_n(z)|^2 |z-a|^{2N c} {\rm e}^{-N |z|^2} \,{\rm
d} A(z)$.
  The compact region $K$ that is the support of the second measure undergoes a
topological transition under the variation of the parameter $t=n/N$; in a
double scaling limit near the critical point given by $t_c=a(a+2\sqrt c)$ we
observe the Hastings-McLeod solution to Painlev\'e\ II in the asymptotics of
the orthogonal polynomials.
