Widely available vegetable oils were readily derivatized into chemically pure ABn-type monomers (n = 2 or 3). Their polymerization led to unprecedented hyperbranched polyesters. Four different AB2/AB3-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 in acidic conditions.