  Let $\tau$n be a random tree distributed as a Galton-Watson tree with
geometric offspring distribution conditioned on {Zn = an} where Zn is the size
of the n-th generation and (an, n $\in$ N *) is a deterministic positive
sequence. We study the local limit of these trees $\tau$n as n $\rightarrow$
$\infty$ and observe three distinct regimes: if (an, n $\in$ N *) grows slowly,
the limit consists in an infinite spine decorated with finite trees (which
corresponds to the size-biased tree for critical or subcritical offspring
distributions), in an intermediate regime, the limiting tree is composed of an
infinite skeleton (that does not satisfy the branching property) still
decorated with finite trees and, if the sequence (an, n $\in$ N *) increases
rapidly, a condensation phenomenon appears and the root of the limiting tree
has an infinite number of offspring.
