Distribution of points of interpolation and of zeros of exact maximally convergent multipoint Pade approximants

Given a regular compact set $E$ in the complex plane, a unit measure $mu$ supported by $partial E,$ a triangular point set $beta := {{beta_{n,k}}_{k=1}^n}_{n=1}^{infty},betasubset partial E$ and a function $f$, holomorphic on $E$, let $pi_{n,m}^{beta,f}$ be the associated multipoint $beta-$ Pade approximant of order $(n,m)$. We show that if the sequence $pi_{n,m}^{beta,f}, ninLambda, m-$ fixed, converges exact maximally to $f$, as $ntoinfty,ninLambda$ inside the maximal domain of $m-$ meromorphic continuability of $f$ relatively to the measure $mu,$ then the points $beta_{n,k}$ are uniformly distributed on $partial E$ with respect to the measure $mu$ as $ ninLambda$. Furthermore, a result about the zeros behavior of the exact maximally convergent sequence $Lambda$ is provided, under the condition that $Lambda$ is dense enough.