  In this paper we investigate the asymptotic behavior of polynomials that are
orthonormal over the interior domain of an analytic Jordan curve L with respect
to area measure. We prove that, inside L, these polynomials behave
asymptotically like a sequence of certain integrals involving the canonical
conformal map of the exterior of L onto the exterior of the unit circle and
certain meromorphic kernel function defined in terms of a conformal map of the
interior of L onto the unit disk. The error term in the integral representation
is proven to decay geometrically and sufficiently fast, allowing us to obtain
more precise asymptotic formulas for the polynomials under certain additional
geometric considerations. These formulas yield, in turn, fine results on the
location, limiting distribution and accumulation points of the zeros of the
polynomials.
