A polymer may have a molecular mass of less than 8,000 g/mol and a polymolecularity index PI of less than 3, produced by free radical polymerization, in water, and at a temperature higher than 50° C., of at least one anionic monomer comprising at least one polymerizable olefinic unsaturation and at least one carboxylic acid function, in the presence of phosphorus with a degree of oxidation I, phosphorus with a degree of oxidation III and a radical-generating compound. Such polymers may be produced and use for grinding mineral matter, as a detergent agent, or as an anti-scaling agent.