  We study site percolation on Angel & Schramm's uniform infinite planar
triangulation. We compute several critical and near-critical exponents, and
describe the scaling limit of the boundary of large percolation clusters in all
regimes (subcritical, critical and supercritical). We prove in particular that
the scaling limit of the boundary of large critical percolation clusters is the
random stable looptree of index 3/2, which was introduced in a companion paper.
We also give a conjecture linking looptrees of any index in (1,2) with scaling
limits of cluster boundaries in random triangulations decorated with O(N)
models.
