A hyperbranched polymer having pendent olefinic groups and comprising polymer units derived from one or more terminally-unsaturated, acyclic aliphatic diene and polymer units derived from maleic anhydride. Optionally, the hyperbranched polymer may further comprise polymer units derived from one or more 1-alkenes and/or a chain transfer agent. A process to prepare the hyperbranched polymer comprises contacting maleic anhydride with at least one terminally unsaturated acyclic aliphatic diene having at least 7 carbon atoms in the presence of an effective amount of a radical initiator in an aprotic solvent under dilute conditions.