Critical points of orthogonal polynomials

We study properties of the critical points of orthogonal polynomials with respect to a measure on the unit circle (OPUC). The main result states that, under some conditions, the asymptotic distribution of the critical points of OPUC coincides with the asymptotic distribution of its zeros and each Nevai-Totik point attracts the same number of critical points as zeros of the OPUC. Analogous results are also presented for paraorthogonal polynomials and for orthogonal polynomials with respect to a regular measure supported on a continuum set.