The invention relates to a copolymer having a backbone that is obtained by radical polymerisation of: a fatty body (A) comprising unsaturations and/or hydroxyl functions； and at least one monomer (B) including at least one function that can be polymerised by means of radical polymerisation and comprising either (i) at least one linear or branched alkyl chain having preferably between 16 and 44 carbon atoms, and more preferably at least 18 carbon atoms, e.g. at least 20 carbon atoms, in particular 22 carbon atoms or 44 carbon atoms, or (ii) a reactive function. The invention also relates to a method for modifying the rheological properties of an non-aqueous medium with the addition of a copolymer of the invention. The invention further relates to a composition formed totally or partially by a copolymer of the invention. Preferably, the composition is an emulsifiable composition. Furthermore, the invention relates to a composition comprising a copolymer of the invention and an emulsifying agent.
