  We study the percolation model on Boltzmann triangulations using a generating
function approach. More precisely, we consider a Boltzmann model on the set of
finite planar triangulations, together with a percolation configuration (either
site-percolation or bond-percolation) on this triangulation. By enumerating
triangulations with boundaries according to both the boundary length and the
number of vertices/edges on the boundary, we are able to identify a phase
transition for the geometry of the origin cluster. For instance, we show that
the probability that a percolation interface has length n decays exponentially
with n except at a particular value p\_c of the percolation parameter p for
which the decay is polynomial (of order n --10/3). Moreover, the probability
that the origin cluster has size n decays exponentially if p < p c and
polynomially if p $\ge$ p\_c. The critical percolation value is p\_c = 1/2 for
site percolation, and p c = 2 $\sqrt$ 3--1 11 for bond percolation. These
values coincide with critical percolation thresholds for infinite
triangula-tions identified by Angel for site-percolation, and by Angel \&
Curien for bond-percolation, and we give an independent derivation of these
percolation thresholds. Lastly, we revisit the criticality conditions for
random Boltzmann maps, and argue that at p\_c , the percolation clusters
conditioned to have size n should converge toward the stable map of parameter 7
6 introduced by Le Gall \& Miermont. This enables us to derive heuristically
some new critical exponents.
