The role of asymmetry on the evolution of prebiotic homochirality is investigated in the context of autocatalytic polymerization reaction networks. A model featuring enantiometric cross-inhibition and chiral bias is used to study the diffusion equations controlling the spatiotemporal development of left and right-handed domains. Bounds on the chiral bias are obtained based on present-day constraints on the emergence of life on early Earth. The viability of biasing mechanisms such as weak neutral currents and circularly polarized UV light is discussed. The results can be applied to any hypothetical planetary platform.