  This work establishes critical phenomena in the topological transition of
black hole coalescence. We describe and validate a computational front tracking
event horizon solver, developed for generic studies of the black hole
coalescence problem. We then apply this to the Kastor - Traschen axisymmetric
analytic solution of the extremal Maxwell - Einstein black hole merger with
cosmological constant. The surprising result of this computational analysis is
a power law scaling of the minimal throat proportional to time. The minimal
throat connecting the two holes obeys this power law during a short time
immediately at the beginning of merger. We also confirm the behavior
analytically. Thus, at least in one axisymmetric situation a critical
phenomenon exists. We give arguments for a broader universality class than the
restricted requirements of the Kastor - Traschen solution.
