Abstract: The question of the origin of homochirality of living matter, or the dominance of one handedness for all molecules of life across the entire biosphere, is a long-standing puzzle in the research on the Origin of Life. In the fifties, Frank proposed a mechanism to explain homochirality based on the properties of a simple autocatalytic network containing only a few chemical species. Following this work, chemists struggled to find experimental realizations of this model, possibly due to a lack of proper methods to identify autocatalysis [1]. In any case, a model based on a few chemical species seems rather limited, because prebiotic earth is likely to have consisted of complex ‘soups’ of chemicals. To include this aspect of the problem, we recently proposed a mechanism based on certain features of large out-of-equilibrium chemical networks [2]. We showed that a phase transition towards an homochiral state is likely to occur as the number of chiral species in the system becomes large or as the amount of free energy injected into the system increases. Through an analysis of large chemical databases, we showed that there is no need for very large molecules for chiral species to dominate over achiral ones; it already happens when molecules contain about 10 heavy atoms. We also analyzed the various conventions used to measure chirality and discussed the relative chiral signs adopted by different groups of molecules [3]. We then proposed a generalization of Frank's model for large chemical networks, which we characterized using random matrix theory. This analysis includes sparse networks, suggesting that the emergence of homochirality is a robust and generic transition. References: [1] A. Blokhuis, D. Lacoste, and P. Nghe, PNAS (2020), 117, 25230. [2] G. Laurent, D. Lacoste, and P. Gaspard, PNAS (2021) 118 (3) e2012741118. [3] G. Laurent, D. Lacoste, and P. Gaspard, Proc. R. Soc. A 478:20210590 (2022).