Let Tn be a random tree distributed as a Galton-Watson tree with geometric offspring distribution conditioned on the size of the n-th generation to be equal to an. We study the local limit of these trees Tn as n goes to infinity observe three distinct regimes: if an 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 increases rapidly, a condensation phenomenon appears and the root of the limiting tree has an infinite number of offspring.