First and second kind paraorthogonal polynomials and their zeros

Given a probability measure @m with infinite support on the unit circle @?D={z:|z|=1}, we consider a sequence of paraorthogonal polynomials h"n(z,@l) vanishing at z=@l where @l@?@?D is fixed. We prove that for any fixed z"0@?supp(d@m) distinct from @l, we can find an explicit @r>0 independent of n such that either h"n or h"n"+"1 (or both) has no zero inside the disk B(z"0,@r), with the possible exception of @l. Then we introduce paraorthogonal polynomials of the second kind, denoted s"n(z,@l). We prove three results concerning s"n and h"n. First, we prove that zeros of s"n and h"n interlace. Second, for z"0 an isolated point in supp(d@m), we find an explicit radius @r@? such that either s"n or s"n"+"1 (or both) have no zeros inside B(z"0,@r@?). Finally, we prove that for such z"0 we can find an explicit radius such that either h"n or h"n"+"1 (or both) has at most one zero inside the ball B(z"0,@r@?).