A generalization to n species of a system by L. Bass, A. J. Bracken, K. Holmaker and B. Jefferies [J. Austral. Math. Soc. (Ser. B) 29 (1987) 156--194], which describes the self-organization of liver zones in a liver capillary in the case of two species, is proposed. We establish some hypotheses on the coefficient parameters of the system under which a part of the species is driven to extinction while the remaining ones are attracted by the non-trivial stationary solution.