What determines the shape of the center-surround receptive fields of retinal ganglion cells?
The center-surround structure is created by the horizontal connectivity of the horizontal cells (Periman et al., 2012)  that receive input from multiple photoreceptors (Fig. 1).


Fig. 1. Retinal patch showing the connectivity between a horizontal cell and photoreceptors. Source: Harvey Mudd College

The horizontal cell passes on the congregate output to the bipolar cell, which in turn drives the retinal ganglion cells (RGCs) that send their axons to the optic nerve and send the signal on its way to the brain.

The photoreceptors are connected in two concentric circles to the horizontal cell. When light stimulation of the inner patch (center) evokes an excitatory response in the RGC, and the outer circle (surround) inhibits this response, the receptive field is said to have an ON-center configuration. In the reverse scenario, it is OFF-center (Fig. 1). This center-surround configuration is one of the first visual processing steps in the visual system and enhances contrast in the perceived image. 


Fig. 2. ON and OFF center-surround receptive fields. Source: Brain Connection 

Reference
- Periman et al., Webvision. The Organization of the Retina and Visual System. Utah