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The peeling process, which describes a step-by-step exploration of a planarmap, has been instrumental in addressing percolation problems on randominfinite planar maps. Bond and face percolation on maps with faces of arbitrarydegree are conveniently studied via so-called lazy-peeling explorations. Duringsuch explorations distinct vertices on the exploration contour may at laterstage be identified, making the process less suited to the study of sitepercolation. To tackle this situation and to explicitly identifysite-percolation thresholds, we come back to the alternative "simple" peelingexploration of Angel and uncover deep relations with the lazy-peeling process.Along the way we define and study the random Boltzmann map of the half-planewith a simple boundary for an arbitrary critical weight sequence. Itsconstruction is nontrivial especially in the "dense regime" where thehalf-planar random Boltzmann map does not possess an infinite simple core.

Simple peeling of planar maps with application to site percolation