During development, one axon typically comes to dominate each set of synaptic sites at a neuromuscular junction. This means that just one neuron controls each muscle fiber, allowing for specificity of motor function.
A nice application of laser irradiation allows researchers to intervene in the formation of axonal branches in developing mice to study this.
What they found was that irradiating the axon currently occupying the site spurred a sequence of events (presumably involving molecular signaling) that led nearby axons (often smaller ones) to take it over.
A 67 second, soundless video of one 1,000-step simulation of this process demonstrates the concepts behind this finding.
In the simulation, each circle represents a synaptic site, and each color an innervating axon. There are originally six colors.
At each of the 1,000 time steps, one axon is withdrawn from a randomly chosen site, and an adjacent one (possibly of the same color) takes it over.
The territory controlled by one axon increases (with negative acceleration) until it comes to dominate all the sites.
Although it is possible that a qualitatively different process occurs for axonal inputs to nerve cells, odds are that a similar sort of evolution via competition helps drive CNS phenomena such as memory. (Because evolution tends to re-use useful processes.)
Turney SG, Lichtman JW (2012) Reversing the Outcome of Synapse Elimination at Developing Neuromuscular Junctions In Vivo: Evidence for Synaptic Competition and Its Mechanism. PLoS Biol 10(6): e1001352. doi:10.1371/journal.pbio.1001352