  Given a regular compact set $E$ in the complex plane, a unit measure $\mu$
supported by $\partial E,$ a triangular point set $\beta :=
\{\{\beta_{n,k}\}_{k=1}^n\}_{n=1}^{\infty},\beta\subset \partial E$ and a
function $f$, holomorphic on $E$, let $\pi_{n,m}^{\beta,f}$ be the associated
multipoint $\beta-$ Pad\'e approximant of order $(n,m)$. We show that if the
sequence $\pi_{n,m}^{\beta,f}, n\in\Lambda, m-$ fixed, converges exact
maximally to $f$, as $n\to\infty,n\in\Lambda$ 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 $ n\in\Lambda$. Furthermore, a result about the zeros
behavior of the exact maximally convergent sequence $\Lambda$ is provided,
under the condition that $\Lambda$ is "dense enough."
