Interpolation characteristics of maximal polynomial approximants to rational functions

Let E be a compact set in C with connected regular complement and let p(n), n is an element of N, be a sequence of polynomials which converge maximally to a fixed rational function f on E. Then p(n) has n + o(n) interpolation points to f in C and the normalized counting measure nu(n) of these interpolation points (resp. its balayage measure (nu) over cap (n) onto the boundary of E) converges to the equilibrium measure of E as n -> infinity. Furthermore, we prove a complete characterization of maximal convergence by interpolation.