Majorizing potentials in strong ratio limit theorems

In this paper, we study the asymptotic properties of the polynomials P _n (z) = P _n (z; f), corresponding to an interpolation table α ? E, where E is a bounded continuum in the complex plane with a connected complement, the table α satisfies the Kakehashi condition, and f is an arbitrary function holomorphic on E. In particular, for zeros of such polynomials, we obtain a generalization of the classical Jentzsch-Szeg? theorem on the distribution of zeros of partial sums of Taylor series.