A thermoplastic block copolymer comprising at least one PA block and at least one PB block, wherein PA represents a polymer block comprising one or more units of monomer A and PB represents a branched-chain polymer block comprising one or more units of monomer B, with monomer A being a vinyl, acrylic, diolefin, nitrile, dinitrile, acrylonitrile monomer, a monomer with reactive functionality, or a crosslinking monomer, and monomer B being a, radically polymerizable triglyceride or mixtures thereof, in the form of a plant oil, animal oil, or synthetic triglycerides, wherein one end or both ends of the PA block or PB block is functionalized with a thiocarbonylthio chain transfer group, wherein said block copolymer has a number average degree of polymerization (N) of up to 100,000 without gelation.