Process for the preparation of aqueous dispersions of (co)polymerizates using a polymer with cationic functionality, optionally accompanied by the use of conventional additives, the polymer with cationic functionality being obtained by (co)polymerization in an aqueous medium of olefinically unsaturated (co)monomers, in which at least one (co)monomer has a cationic functionality, further (co)monomers are added and polymerization takes place in the presence of suitable initiators, wherein the polymers and/or (co)monomers are so chosen and the process is so controlled that a (co)polymerizate particle with heterogeneous morphology is formed and the dispersed (co)polymerizate obtained has a glass transition temperature Tg of more than about 50.degree. C. The invention also relates to a process in which the polymer with cationic functionality is formed in situ in the presence of a seed. Redispersible powders and the use thereof are also described.