Equilibrium measure and the distribution of zeros of the extremal polynomials of a discrete variable

The problem of the limiting distribution of the zeros of the polynomial extremal in the $L^2$-metric with respect to a measure with finitely many points of growth is studied under the assumption that the degree $n$ of this polynomial and the number $N$ ($N>n$) of points of growth of the measure approach infinity so that $n/N\to c\in (0,1)$.