Methods of preparing prepolymers with M = (2–5) × 10(4) via the free-radical polymerization of methyl methacrylate in the presence of tri-n-butyl boron and 1,4-naphthoquinone at 30–45°C are developed. 1H NMR spectroscopy measurements show that, in the prepolymer, the ratio between the enchained aromatic structures and the monomer units is 3: 1000. The activation energy for the postpolymerization of MMA initiated by the prepolymer is found to be 39.3 kJ/mol, and the molecular mass of the prepolymer is (0.8–1.2) × 106. The effect of small amounts of acrylates and phosphonium salts on the polymerization of methyl methacrylate and the molecular mass of the polymers is investigated. It is demonstrated that, when polymerization is conducted in the presence of ionic liquids at concentrations commensurable with the concentration of aromatic fragments enchained into the prepolymer, the rate of the process decreases.