We have studied both experimentally and theoretically how the presence of polymer fibrils can influence the ordering in liquid crystal systems. When such fibrils are formed by polymerization in a nematic solution, the polymer structure can reflect the director orientation at the time of polymerization. This anisotropic structure can be retained even when the liquid crystal is heated into its isotropic phase. We report measurements of this effect and also calculations based on a simple model of the mechanism by which the polymer fibrils can be expected to influence the nematic order of a liquid crystal matrix. A numerical solution of the theoretical model suggests that the discontinuity in order parameter that occurs at the transition temperature should gradually diminish as polymer concentration is increased and should vanish at a critical concentration. This is in agreement with our experimental observations.