Abstract: The invention relates to a star block copolymer of the formula [S.sub.1 -S.sub.2 -(B.sub.1 /S.sub.3)-B.sub.2 ].sub.m -X-[B.sub.2 (B.sub.1 /S.sub.3)-S.sub.2 ].sub.n in which X represents a polyfunctional radical resulting from a coupling agent, m and n represent non-zero integers such that m+n is equal to 3 or 4, S.sub.1 and S.sub.2 each represent a block of a polymer containing at least one vinylaromatic monomer, B.sub.2 represents a block of a polymer containing at least one conjugated diene, (B.sub.1 /S.sub.3) represents a block of a statistical copolymer containing at least one vinylaromatic monomer and at least one conjugated diene, 40 to 75% by weight of (B.sub.1 /S.sub.3) consisting of resulting from vinylaromatic monomer, characterized in that the sum of the mass of the blocks B.sub.2 contains more than 40% by weight and less than 90% by weight of the total mass of the conjugated diene contained in the said star block copolymer. The invention also relates to the process for obtaining this copolymer.

Abstract: A process for manufacturing block copolymers comprising anionically polymerizing a vinyl aromatic hydrocarbon mononer in solution in an aromatic hydrocarbon solvent capable of giving a homogeneous medium until attaining a homogeneous medium with a viscosity greater than 300 Pa.s at 20.degree. C. for a concentration of polymer in the aromatic hydrocarbon solvent between 60 and 90% by weight and then, after introduction of a conjugated diene, carrying out a copolymerization until a homogeneous medium is attained have a viscosity greater than 300 Pa.s at 90.degree. C. for a concentration of copolymer in the aromatic hydrocarbon solvent between 70 and 90% by weight, without the viscosity exceeding 3,000 Pa.s in either of the two polymerization steps.