The invention relates to a redispersible powder obtainable by (co)polymerization, using a polymer with cationic functionality in an aqueous medium, 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, wherein at least one (co)monomer has a cationic functionality, further (co)monomers are added and polymerization takes place in the presence of suitable initiators, and by drying the aqueous dispersion obtained, the (co)polymerizate having one or more reactive groups. According to another embodiment, the polymer with cationic functionality is formed in situ in the presence of a seed. According to another embodiment, the process is controlled in such a way that a (co)polymerizate particle with heterogeneous morphology is formed. The invention also relates to the aqueous dispersions, a process for the preparation of the redispersible powder and the use thereof.