The invention provides compositions of matter, methods of their synthesis, and methods of their use in polymerization reactions. The compositions include polyfunctional initiators used to make star polymers when polymerized with monomers. The polyfunctional initiators are synthesized out of a multifunctional core with at least two functional groups and two or more initiator units bonded to the functional groups. The initiator units have two electron-withdrawing groups bonded to a central carbon atom and an azo group between the central carbon atom and the functional group. The polyfunctional initiators are particularly effective because when they decompose to form the radical core of a star polymer, the electron-withdrawing groups prevent the corresponding radical from forming any linear polymer contamination and only desired star polymers result.