The invention concerns the polymers obtained by the use of sulphur compounds in a process for controlled radical polymerisation in water of acrylic acid and/or acrylic acid with hydrosoluble monomers. It concerns also their uses as dispersant agents or agents to aid grinding and/or co-grinding of mineral matters in aqueous suspensions, and as dispersant agents incorporated directly in aqueous formulations containing mineral matters. Finally, the invention concerns the formulations of mineral matters obtained in this manner.