  We study a particular type of subcritical Galton--Watson trees, which are
called non-generic trees in the physics community. In contrast with the
critical or supercritical case, it is known that condensation appears in
certain large conditioned non-generic trees, meaning that with high probability
there exists a unique vertex with macroscopic degree comparable to the total
size of the tree. Using recent results concerning subexponential distributions,
we investigate this phenomenon by studying scaling limits of such trees and
show that the situation is completely different from the critical case. In
particular, the height of such trees grows logarithmically in their size. We
also study fluctuations around the condensation vertex.
