  The zeros of semi-orthogonal functions with respect to a probability measure
mu supported on the unit circle can be applied to obtain Szego quadrature
formulas. The discrete measures generated by these formulas weakly converge to
the orthogonality measure mu. In this paper we construct families of
semi-orthogonal functions with interlacing zeros, and give a representation of
the support of mu in terms of the asymptotic distribution of such zeros.
