In this presentation, we will first study the limit behavior of a Bienaymé-Galton-Watson (BGW) tree conditioned to have n vertices and k leaves, where k is fixed and n goes to infinity.

Then, we will consider the case where the BGW tree is conditioned to have n vertices and k internal nodes.

We will show that in this configuration, unlike the first case, the shape of the limiting tree varies depending on properties of the offspring distribution.