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We obtain a very simple formula for the generating function of bipartite(resp. quasi-bipartite) planar maps with boundaries (holes) of prescribedlengths, which generalizes certain expressions obtained by Eynard in a book toappear. The formula is derived from a bijection due to Bouttier, Di Francescoand Guitter combined with a process (reminiscent of a construction of Pitman)of aggregating connected components of a forest into a single tree. The formulanaturally extends to $p$-constellations and quasi-$p$-constellations withboundaries (the case $p=2$ corresponding to bipartite maps).

A simple formula for the series of constellations and quasi-constellations with boundaries