  We introduce a dbar-formulation of the orthogonal polynomials on the complex
plane, and hence of the related normal matrix model, which is expected to play
the same role as the Riemann-Hilbert formalism in the theory of orthogonal
polynomials on the line and for the related Hermitian model. We propose an
analog of Deift-Kriecherbauer-McLaughlin-Venakides-Zhou asymptotic method for
the analysis of the relevant dbar-problem, and indicate how familiar steps for
the Hermitian model, e.g. the g-function ``undressing'', might look like in the
case of the normal model. We use the particular model considered recently by P.
Elbau and G. Felder as a case study.
