A copolymer that includes for 100 mol %: a) more than 70 mol % and up to 99.9 mol % of hydrophobic monomer units (A) from stearyl methacrylate; and b) 0.1 mol % to 30 mol % of monomer units (B) from at least one monomer of a compound of formula (I) where R1 is a linear or branched alkyl radical comprising 12 to 22 carbon atoms, R2 is a hydrogen atom or a methyl radical, and n is an integer greater than or equal to 0 and lower than or equal to 30, wherein it is understood that said compound of formula (I) is not stearyl methacrylate. The invention also relates to a method for preparing and using same as a modifier of the rheology of the oil phase of a topical cosmetic, dermopharmaceutical, or pharmaceutical composition.