The invention relates to the use of a slightly anionic and water-soluble copolymer, as a dispersing agent and/or an agent for assisting the grinding of pigments and/or mineral fillers in aqueous suspension giving on the one hand a low Zeta potential to the aqueous suspensions of the said fillers and/or pigments and on the other hand affording an electro-steric stabilisation of the said suspensions. The invention also relates to the said aqueous suspensions of mineral pigments and/or fillers and their uses in the fields of paper, such as the manufacture or coating of paper, and drilling muds used for petroleum prospecting or extraction. The invention also relates to the use of the said dispersing agents and/or agent for assisting the grinding in the field of paints and plastic materials such as thermoplastic or thermosetting resins.