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Barium (Ba) stars are polluted by material enriched in the slow neutron capture (s-process) elements synthesised in the interior of their former asymptotic giant branch (AGB) companion star, which is now a white dwarf. We compare individual Ba star abundance patterns to AGB nucleosynthesis models to verify if the AGB model mass is compatible with independently derived AGB mass. We selected a sample of 28 Ba stars for which both self-consistent spectroscopic observation and analysis are available and stellar mass determinations, via positioning the star on the HR diagram and comparing with evolutionary tracks. For this sample stars we considered both previously and recently derived elemental abundances. Then, we performed a detailed comparison of these s-process elemental abundances to different AGB nucleosynthesis models from the Monash and the FRUITY theoretical data sets. We simplified the binary mass transfer by calculating dilution factors to match the [Ce/Fe] value of each star when using different AGB models, and we then compared the diluted model abundances to the complete Ba-star abundance pattern. Our comparison confirms that low mass, non-rotating AGB stellar models with 13C as the main neutron source are the polluters of the vast majority of the considered Ba stars. Out of the 28 stars, in 21 cases the models are in good agreement with both the determined abundances and the independently derived AGB mass, although in 16 cases higher observed abundances of Nb, Ru, Mo and/or Nd, Sm than predicted. For 3 stars we obtain a match to the abundances only by considering models with masses lower than those independently determined. Finally, 4 stars show much higher first s-process peak abundance values than the model predictions, which may represent the signature of a physical and/or nucleosynthetic process that is not represented in the set of models considered here.