We provide a complete picture of the local convergence of critical or
subcritical Galton-Watson tree conditioned on having a large number of
individuals with out-degree in a given set. The generic case, where the limit
is a random tree with an infinite spine has been treated in a previous paper.
We focus here on the non-generic case, where the limit is a random tree with a
node with infinite out-degree. This case corresponds to the so-called
condensation phenomenon.