  An asymptotic formula for the Tian-Paul CM-line of a flat family blown-up at
a flat closed sub-scheme is given. As an application we prove that the blow-up
of a polarized manifold along a (relatively) Chow-unstable submanifold admits
no (extremal) constant scalar curvature Kahler metrics in classes making the
exceptional divisors sufficiently small. Moreover a geometric characterization
of relatively Chow-unstable configuration of points in the projective space is
given. From this we get new examples of classes admitting no extremal Kahler
metric also in the case of the projective plane blown-up at a finite set of
points.
