  We prove that there is a universal measure on the unit circle such that any
probability measure on the unit disk is the limit distribution of some
subsequence of the corresponding orthogonal polynomials. This follows from an
extension of a result of Alfaro and Vigil (which answered a question of
Tur\'an): namely, for $n<N$, one can freely prescribe the $n$-th polynomial and
$N-n$ zeros of the $N$-th one. We shall also describe all possible limit sets
of zeros within the unit disk.
