  We study the scaling limit of the volume and perimeter of the discovered
regions in the Markovian explorations known as peeling processes for infinite
random planar maps such as the uniform infinite planar triangulation (UIPT) or
quadrangulation (UIPQ). In particular, our results apply to the metric
exploration or peeling by layers algorithm, where the discovered regions are
(almost) completed balls, or hulls, centered at the root vertex. The scaling
limits of the perimeter and volume of hulls can be expressed in terms of the
hull process of the Brownian plane studied in our previous work. Other
applications include the metric exploration of the dual graph of our infinite
random lattices, and first-passage percolation with exponential edge weights on
the dual graph, also known as the Eden model or uniform peeling.
