  We define and analyze a coalescent process as a recursive box-filling process
whose genealogy is given by an ancestral time-reversed, time-inhomogeneous
Bienyam\'{e}-Galton-Watson process. Special interest is on the expected size of
a typical box and its probability of being empty. Special cases leading to
exact asymptotic computations are investigated when the coalescing mechanisms
are either linear-fractional or quadratic.
