We use a focused ultraviolet (UV) laser beam to photopolymerize localized polymer networks in a cholesteric liquid-crystalline host and to thereby stabilize small, light-diffracting "fingerprint'' domains within a uniform, planar-aligned sample. As we have previously described, these "microspot'' gratings are electrically switchable [1] and can be produced with diameters ranging from a few tens to hundreds of microns. Our focus in this article is to model the growth of the stabilized domain using a simple reaction-diffusion model of the photopolymerization process and to compare this model with data for networks formed both from isotropic and mesogenic monomers. In spite of an initial spatial asymmetry observed in the mesogenic case, both types of light-controlled networks develop in accordance with the fast photoreactivity/weak diffusion limit of the model.