  In the study of the cyclicity of a function $f$ in reproducing kernel Hilbert
spaces an important role is played by sequences of polynomials $\{p_n\}_{n\in
\mathbb{N}}$ called \emph{optimal polynomial approximants} (o.p.a.). For many
such spaces and when the functions $f$ generating those o.p.a. are polynomials
without zeros inside the disk but with some zeros on its boundary, we find that
the weakly asympotic distribution of the zeros of $1-p_nf$ is the uniform
measure on the unit circle.
