Widely available vegetable oils were readily derivatized into chemically pure AB(n)-type monomers (n = 2 or 3). Their polymerization led to unprecedented hyperbranched polyesters. Four different AB(2)/AB(3)-type monomers bearing one A-type methyl ester and two or three B-type alcohol functions were purposely synthesized via two elementary steps, i.e. epoxidation of the internal double bond of the vegetable oil precursors followed by ring-opening of the epoxy groups under acidic conditions. The polycondensation of these bio-sourced monomers was performed in bulk, in the presence of an appropriate catalyst, giving access to modular hyperbranched polyesters with tunable properties. Among the catalysts tested, zinc acetate, 1,5,7-triazabicyclo[4.4.0]dec-5-ene (TBD) and sodium methoxide proved the most effective, allowing the achievement of molar masses in the range 3000-10 000 g mol(-1) and dispersities varying from 2 to 15, depending on the initial conditions. The degree of branching, DB, as determined by H-1 NMR spectroscopy, was found to be between 0.07 and 0.45. The as-devised hyperbranched polyesters displayed either amorphous or semi-crystalline properties, as a function of the selected AB(2)/AB(3)-type initial monomers, with a glass transition temperature, T-g, ranging from -33 to 9 degrees C and a decomposition temperature at 5 wt% of the sample, T-d5%, varying from 204 to 340 degrees C.