  We resolve the fate of the two original apparent horizons during the head-on
merger of two non-spinning black holes. We show that following the appearance
of the outer common horizon and subsequent inter-penetration of the original
horizons, they continue to exist for a finite period of time before they are
individually annihilated by unstable MOTSs. The inner common horizon vanishes
in a similar, though independent, way. This completes the understanding of the
analogue of the event horizon's "pair of pants" diagram for the apparent
horizon. Our result is facilitated by a new method for locating marginally
outer trapped surfaces (MOTSs) based on a generalized shooting method. We also
discuss the role played by the MOTS stability operator in discerning which
among a multitude of MOTSs should be considered as black hole boundaries.
