  We show that interpolation results in the $S$-nodes theory may be considered
as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur)
coefficients occurs in Khrushchev formulas, the separation of the so the called
new Verblunsky-type coefficients occurs in the interpolation formulas of the
$S$-nodes theory. General asymptotic inequalities (and equalities) for the
$S$-nodes, with application to the block Hankel matrices, are derived using
this approach. Another asymptotic inequality, needed in the proofs and
important in itself, is derived in Appendix B.
