The invention relates to a method for the controlled radical polymerisation of acrylic acid and the salts thereof in a reaction medium consisting only of water. The invention also relates to the acrylic acid homopolymers and copolymers obtained using said polymerisation method. The invention further relates to the use of the aforementioned acrylic acid homopolymers and copolymers in industries such as paper and, in particular, paper coating and paper filling, the oil sector and in the fields of painting, water treatment, detergency, ceramics, cements and hydraulic binders, civil engineering, inks and varnishes, textile sizing and leather finishing.