The present invention relates to a process for controlled radical polymerization using an organosulfur reversible chain transfer agent which consists in preparing polymers having a molar weight of greater than 100 000 g/mol, with a polydispersity index of less than 1.2 for molar weights of less than 200 000 g/mol and of less than 1.4 for molar weights of greater than 200 000 g/mol, with a degree of conversion of monomer of greater than 75% and a polymerization time of less than 8 h, characterized by the control of the flux of initiator radicals in the polymerization medium.