  We consider extremal polynomials with respect to a Sobolev-type $p$-norm,
with $1<p<\infty$ and measures supported on compact subsets of the real line.
For a wide class of such extremal polynomials with respect to mutually singular
measures (i.e. supported on disjoint subsets of the real line), it is proved
that their critical points are simple and contained in the interior of the
convex hull of the support of the measures involved and the asymptotic critical
point distribution is studied. We also find the $n$th root asymptotic behavior
of the corresponding sequence of Sobolev extremal polynomials and their
derivatives.
