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The esterification of oleic acid was applied in order to screen the suitability of a series of phosphotungstic-based Wells-Dawson types of compounds as potential catalysts in the heterogeneous transesterification of sunflower waste cooking oil. This test reaction indicated that the phosphotungstic Wells-Dawson heteropolyacid H6P2W18O62·xH2O, dispersed on titania oxide in a loading of 15 mg per m2 of oxide support (named 42% HPA/TiO2) and possessing exclusively Brønsted acid sites, was the most promising among the screened materials. In addition, the application of a nonlinear analysis methodology to find a surface that fits the specific activity of the oleic acid esterification with methanol at various temperatures, weights of catalyst, molar ratios of substrates, and stirring speeds, and also considering the active phase desorption out of the catalyst's surface, allowed determining the optimum operative conditions that were applied in the transesterification of the waste cooking oil afterwards. The transesterification of the waste cooking oil at 60 °C and 1:9 WCO: methanol molar ratio in a batch reactor under stirring at 650 rpm for 3 h, catalyzed with 0.25 wt% of 42% HPA/TiO2 (20.0 g of oil and 49.6 mg of catalyst), presents 74.6% of conversion of glycerides and 74.4% yield towards fatty acid methyl esters. The catalyst was recovered and reused several times, maintaining a fairly constant catalytic performance. [ABSTRACT FROM AUTHOR]