random planar maps. They are known as *stable maps* and were first obtained by Le Gall and Miermont [@LM11; @LM10 and references therein], by considering very specific distributions for the degree of a typical face, that have infinite variance (see also [@M18] for the same scaling limits under relaxed hypotheses). However, only the Brownian map has been characterized yet, in the sense that for other stable maps, the uniqueness of the scaling limit is not yet proven.

Similarly as in the Brownian case, the authors in [@BBCK16] were able to extend the geometrical connection previously mentioned, to holes’ perimeters in discrete approximations of stable disks and plane (in the so-called *dilute case*) and a specific family of self-similar growth-fragmentations.

There is a natural way of measuring the “size” of these stable surfaces, namely, the so-called *intrinsic volume measure*, which can be constructed as the scaling limit of the number of vertices (or faces) in the approximation by discrete random maps. This measure corresponds to the intrinsic area measure in the related growth-fragmentation; we shall rather use this name since we consider planar objects.

Besides being aesthetic, this connection has already been fruitful in both directions: for instance, it allowed the 