It has been proposed that the terminal arbors of retinal ganglion cells continually shift positions in the optic tectum as a natural consequence of growth in larval amphibians and teleost fish. Here, we develop a detailed anatomical model of this process, based on recent observations in goldfish. The model predicts some unusual structural features of optic axons in the tectum. It was tested in two ways by use of the tracer, horseradish peroxidase (HRP). In the first, optic axons in the tectum were visualized by anterogradely transported HRP applied in the nerve or retina. As predicted, the axons had three parts: (1) fascicular segment (in the stratum opticum), (2) extrafascicular segment (in the synaptic neuropil), and (3) terminal arbor (also in the neuropil). The extrafascicular segment extended up to 1 mm caudally from the fascicle through which it entered the tectum. At its terminus, the arbor was restricted to a single lamina in which it branched extensively over an elliptical area with major axes between 100 and 200 micron long. In the second test, retinal ganglion cell bodies were labeled by retrogradely transported HRP applied to the tectum in a manner intended to label all axons and terminals in the vicinity. The pattern and locations of labeled cells varied, depending on where the HRP was applied, in detailed accord with the model's predictions. The close agreement between the model and the observations supports the hypothesis of shifting terminals.