  Stack triangulations appear as natural objects when defining an increasing
family of triangulations by successive additions of vertices. We consider two
different probability distributions for such objects. We represent, or "draw"
these random stack triangulations in the plane $\R^2$ and study the asymptotic
properties of these drawings, viewed as random compact metric spaces. We also
look at the occupation measure of the vertices, and show that for these two
distributions it converges to some random limit measure.
