There are disclosed star shaped thermoplastic elastomers made of acrylic block copolymers obtained by transition metal catalysed radical polymerisation. The elastomers comprise core arms obtained from monomers or mixture of monomers, whose T.sub.g is from about -65.degree. C. to about -20.degree. C., and of shell arms obtained from monomers or mixture of monomers, whose T.sub.g is from about 70.degree. C. to about 160.degree. C. The core copolymer has a polydispersity of 2 or higher and the final copolymer has a polydispersity of from 3 to 10.