AbstractComb polymers were prepared by reacting a poly(ethylene‐alt‐maleic anhydride) with alkyl amines or poly(ethylene glycol) (PEG) amines. The resulting polymers were used to modify bleached softwood kraft pulp fibre surfaces by catalyst‐free grafting in a process suitable for pulp mill implementation. Pulp fibres were impregnated with a polymer solution and cured above 100°C. High grafting yields were obtained despite having up to 88% of the anhydride groups consumed by amine derivatization. Grafting yields were more than 90% when the polymer dosage was <13 g/kg (dry polymer/dry fibre) for alkyl derivatives and < 38 g/kg for PEG derivatives. We propose that the upper dosage limit for efficient grafting reflects the need for direct contact between cellulose and every polymer chain for ester linkage formation. For a given polymer dosage, the cured pulp sheets had a maximum wet tensile index, TImax, when either curing time or temperature was increased. Both the alkyl and PEG derivatives fit the power law for the wet TImax~βΓru0.54–0.62 where β values were the estimated conversion of succinic acid moieties to anhydrides when the pulp sheets were cured, and Γru is the dimensionless polymer content that is numerically equal to the amount of applied polymer in mmol repeat units/g dry fibre. However, high polymer dosages give experimental TImax values that fall below the power law, irrespective of curing intensity, because the pulp sheets contain unfixed polymer chains that lubricate fibre/fibre joints, lowering wet strength.