  This is a continuation of the work of Arezzo-Pacard-Singer and the author on
blowups of extremal K\"ahler manifolds. We prove the conjecture stated in [32],
and we relate this result to the K-stability of blown up manifolds. As an
application we prove that if a K\"ahler manifold M of dimension greater than 2
admits a cscK metric, then the blowup of M at a point admits a cscK metric if
and only if it is K-stable, as long as the exceptional divisor is sufficiently
small.
