  We consider the orthogonal polynomials, $\{P_n(z)\}_{n=0,1,\cdots}$, with
respect to the measure $$|z-a|^{2c} e^{-N|z|^2}dA(z)$$ supported over the whole
complex plane, where $a>0$, $N>0$ and $c>-1$. We look at the scaling limit
where $n$ and $N$ tend to infinity while keeping their ratio, $n/N$, fixed. The
support of the limiting zero distribution is given in terms of certain
"limiting potential-theoretic skeleton" of the unit disk. We show that, as we
vary $c$, both the skeleton and the asymptotic distribution of the zeros behave
discontinuously at $c=0$. The smooth interpolation of the discontinuity is
obtained by the further scaling of $c=e^{-\eta N}$ in terms of the parameter
$\eta\in[0,\infty).$
