  We study the asymptotics of the $L^2$-optimal holomorphic extensions of
holomorphic jets associated with high tensor powers of a positive line bundle
along submanifolds.
  More precisely, for a fixed complex submanifold in a complex manifold, we
consider the operator which for a given holomorphic jet along the submanifold
of a positive line bundle associates the $L^2$-optimal holomorphic extension of
it to the ambient manifold. When the tensor power of the line bundle tends to
infinity, we give an explicit asymptotic formula for this extension operator.
This is done by a careful study of the Schwartz kernels of the extension
operator and related Bergman projectors. It extends our previous results, done
for holomorphic sections instead of jets.
  As an application, we prove the asymptotic isometry between two natural norms
on the space of holomorphic jets: one induced from the ambient manifold and
another from the submanifold.
