Zero distribution of incomplete Padé and Hermite–Padé approximations

We prove that a subsequence of the normalized zero counting measures of incomplete Padé approximants tend, as the degree of the numerators goes to infinity and that of the denominators remains bounded, to the uniform distribution on the largest circle centered at the origin inside of which the approximants converge in the sense of the Hausdorff content. As a consequence, a Jentzsch–Szegő type theorem for row sequences of Hermite–Padé approximants is given.