AbstractSynapse elimination at the vertebrate neuromuscular junction reduces a polyinnervated population of muscle fibers to a monoinnervated state. The function of this developmental phenomenon (if any) is unproven. A theoretical analysis of Hebbian (correlation) rules connecting presynaptic and postsynaptic activity and synaptic strength at the neuromuscular junction is presented. The following points are demonstrated: (1) Correlational competition leads to the reduction of polyinnervation to a stable monoinnervated state; (2) the competition gives rise to the size principle over a wide range of the plausible parameter space; (3) over a significant subrange, the competition selectively eliminates topographically incorrect synapses; and (4) in cases in which topographic projection errors overwhelm the system, both error correction and the development of the size principle are disrupted. Correlational competition may explain contradictory experimental results concerning the effects of stimulating or silencing subpopulations of motor neurons. It may also explain an otherwise puzzling instance of a breakdown in the size principle seen in humans undergoing neural regeneration. Taken together, these findings suggest a novel hypothesis for the function of synapse elimination at the neuromuscular junction: the establishment of the size principle. © 1995 John Wiley & Sons, Inc.