A model for the oxidation of carbon monoxide on a fractal surface, in a square lattice of size L × L (L ≤ 240), is simulated by means of the Monte-Carlo technique. The employed model, based on the Langmuir-Hinshelwood reaction mechanism, has a single parameter, namely the mole fraction of CO in the gas phase (pCO). Since simulations start with uncovered surfaces, a transient period always precedes the stationary regime of the reaction. A reactive steady state with CO2 production is only found within a narrow window of pCO which depends on the size of the sample. Outside the reaction window the surface becomes self-poisoned by the reactants. Extrapolation to L = ∞ gives 0.314 < PCO < 0.408 for the reaction window while for L ≤ 30 ± 5 the reactions always by self-poisoning. It is shown that oxidation events mostly take place at the border between O and CO islands, so the rate of CO2 production (RCO) becomes proportional to (1 - θO - θCO) where θO and θCO are the coverages of oxygen and CO, r dependence of RCO on both θO and θCO also holds for the transient period. Also, RCO exhibits a peak close to the window where precisely the length of the border between O and CO islands becomes maximum. The role played by fluctuations of the size of CO and oxygen islands on the self-poisoning of small samples is also discussed. © 1990.