A common problem of non-enzymatic artificial replicator systems is product inhibition leading to parabolic instead of exponential amplification. Exponential chemical replication of oligonucleotides was recently achieved by an iter- ative, stepwise procedure, which employs the surface of a solid support, and which was called SPREAD (i.Surface Promoted Replication and Exponential Amplification of DNA analoguesli). We here report on theoretical insights into the design of an autonomous variant of the SPREAD procedure. The corresponding program simulates a given set of chemical reactions coupled to a chromatographic process where the chromatographic column is treated as a se- ries of connected cells. The crucial step is a template-directed reaction occurring at the surface: Thus, we assumed that two parabolic replicators compete for their building blocks in the chromatographic column. A simplified, semi-analytic treatment confirms that competing parabolic replicators that spread on mineral surfaces are amenable for Darwinian selection under a wide range of parameter values. We believe that the chromatographized replicator model is relevant to the origin of life on earth. The chromatographic column is equivalent to a tunnel or a riverbed of minerals in which water containing the resources is continuously running through.