Motivated by an alternative to the concept of a prebiotic soup in the form of interacting crystal growth close to hot vents, we investigate a model system in which the growth rate of a particular entity is modified (enhanced or reduced) by other entities present, thus forming a web of cross catalysis. Initially random interactions are imposed, but the entities compete for a common source, and some entities may thus vanish in the competition. New entities, or mutations (error copies), with randomly selected interactions to the web are then introduced, and the concentrations of the entities are followed as solutions to stiff ordinary differential equations. Entities with positive growth may create new related entities with slightly randomly modified interactions to the web. Extinctions, wild-type survival and replacement, and self-organization to sustain periodic external variations, are studied. It is shown that even systems with mostly cross-inhibition and no initial autocatalysis may eventually create highly stable self-organized systems. We find that an already established cross catalyzed system often wins over a selfreplicating invader (or mutant).