Local club condensation in extender models

Local club condensation is an abstraction of the condensation properties of the constructible hierarchy.
We will prove that for extender models that are countably iterable, given a cardinal kappa, the J_alpha^{E} hierarchy witnesses local club condensation in the interval (kappa^+,kappa^++) if and only if kappa is not a subcompact cardinal in L[E]. 

From the above and the equivalence between subcompact cardinals and square, due to Schimmerling and Zeman, it follows that in such extender models \square_kappa holds iff the J_alpha^{E} hierarchy witnesses that local club condensation holds in the interval (kappa^+,kappa^++).