uniformly distributed $q$-angulations with $n$ faces of the sphere [@L13; @M13]. Similarly, Brownian disks are random compact metric spaces homeomorphic to the unit disk of $\mathbb{R}^2$, obtained as scaling limits of random planar maps with a boundary [@BM17]. In [@CL14], the Brownian plane, locally isomorphic to the Brownian map, is obtained as scaling limits of the UIPQ and uniform quadrangulations. Moreover it can also be seen as the Gromov-Hausdorff tangent cone of the Brownian map at its root.

In [@BCK15], it was shown that the collection of perimeters of the holes observed when slicing Boltzmann triangulations at all heights converges, when properly rescaled, towards a particular self-similar growth-fragmentation. We also mention Theorems 3 and 23 of Le Gall and Riera [@LR18], which show that, when slicing directly the free Brownian disk, the holes’ perimeters are described by the same growth-fragmentation as in [@BBCK16] (see also [@MS15] Section 4). When $\mathbf{X}$ starts from a single cell of size 0 that grows indefinitely, the geometrical connection corresponds this time to the holes in a sliced discrete approximation of the Brownian plane.

There is actually a broader family of continuum random surfaces, with different scaling exponents, that arise as limiting objects of Boltzmann 