We often seek to understand a group through the distribution of its orbits on a given space. In this talk we will follow Ledrappier's ideas to study the distribution of lattice orbits. He shows that such distribution can be deduced, using a thickening trick, from the equidistribution of the unipotent flow. These ideas were used in a variety of groups, and we will see what are the difficulties that arise when discussing a geometrically finite group. This is based on a joint work with Jacqueline Warren. Speaker(s): Nattalie Tamam (U Michigan)