This work describes studying the permanent grafting of carboxylic acid end-functionalized poly(ethylene glycol) methyl ether (PEG) chains of different molecular weights from the melt onto a surface employing poly(glycidyl methacrylate) ultrathin film as an anchoring layer. The grafting led to the synthesis of the complete PEG brushes possessing exceptionally high grafting density. The maximum thickness of the attached PEG films was strongly dependent on the length of the polymer chains being grafted. The maximum grafting efficiency was close to the critical entanglement molecular weight region for PEG. All grafted PEG layers were in the "brush regime", since the distance between grafting sites for the layers was lower than the end-to-end distance for the anchored macromolecules. Scanning probe microscopy revealed that the grafting process led to complete PEG layers with surface smoothness on a nanometric scale. Practically all samples were partly or fully covered with crystalline domains that disappeared when samples were scanned under water. Due to the PEG hydrophilic nature, the surface with the grafted layer exhibited a low (up to 21degrees) water contact angle.