Process for the preparation of impact-strengthened cast PMMA sheets comprising the following stages: 1. a mixture comprising: at least one alkoxyamine Z(-T)n, in which Z denotes a polyvalent group and n an integer greater than 2, preferably of between 2 and 10, advantageously between 2 and 8, and the monomer(s) intended to form a central block B is heated to a temperature sufficient to activate the alkoxyamine and polymerize the monomer(s); 2. the central block B, optionally mixed with the unconsumed monomer(s) from stage 1, is reactivated in the presence of the monomer(s) intended to form the branches A; 3. MAM and optionally at least one comonomer M which can be copolymerized by the radical route with MMA and at least one radical initiator are added to the mixture obtained in stage 2; 4. the mixture from stage 3 is cast in a mould and then heated.