A three‐dimensional system of ordinary differential equations of first order has been proposed to describe the kinetics of a model tribopolymerization process for which a linear coupling of the material surface dislocation density and polyreaction fields is assumed. Another important physical motivation on which the model is based stresses the predominant role of a highly rough surface under friction as a catalyst in the polyreaction process. In consequence, the fractal‐like chemical reaction concept has been applied. It is demonstrated that the system proposed is suitable for describing a variety of tribopolymerization processes and possesses non‐trivial time‐dependent behaviour even in some limiting analytical cases studied. As a specific result, a nonlinear equation generalizing the Vogel–Fulcher temperature‐dependence of the maximum time scale for the polyreaction caused by friction, characteristic of the selective transfer during friction process, has been recovered. Some comparison with an approach made earlier (G.P. Shpenkov, Friction Surface Phenomena (Elsevier, Amsterdam, 1995) pp. 165–172 and Ref. [239] therein) has been presented as well. Certain basic trends of modelling and experiment are in good agreement.