We have developed a highly versatile universal approach to grow polymer brushes from a variety of substrates with high grafting density by using a single-component system. We describe a random copolymer which consists of an inimer, p-(2-bromoisobutyloylmethyl)-styrene (BiBMS), copolymerized with glycidyl methacrylate (GMA) synthesized by reversible addition fragmentation chain-transfer (RAFT) polymerization. Thermal cross-linking created a mat that was stable during long exposure in organic solvent even with sonication or during Soxhlet extraction. The absolute bromine density was determined via X-ray photoelectron spectroscopy (XPS) to be 1.86 +/- 0.12 Br atoms/nm(3). The ratio of experimental density to calculated absolute initiator density suggests that similar to 25% of the bromine is lost during cross-linking. Surface-initiated ATRP (SI-ATRP) was used to grow PMMA brushes on the substrate with sacrificial initiator in solution. The brushes were characterized by ellipsometry, XPS, and atomic force microscopy (MM) to determine thickness, composition, and homogeneity. By correlating the molecular weight of polymer grown in solution with the brush layer thickness, a high grafting density of 0.80 +/- 0.06 chains/nm(2) was calculated. By synthesizing the copolymer before cross-linking on the substrate, this single-component approach avoids any issues with blend miscibility as might be present for a multicomponent curable mixture, while resulting in high chain density on a range of substrates.