We will talk about the non-existence of infinite cluster in a family of random "out degree 1" graph built on a Poisson point process in $R^d$. We will present two assumptions such that, each geometric "out degree 1" graph satisfying these two rules does not admit an infinite cluster with probability one. We will focus on a "growthsegment model" defined by G. Last, wich is an example of "out degree 1" graph satisfying our two assumptions.