The present invention provides novel methods of fabricating microelectronics structures, and the resulting structures formed thereby, using EUV lithographic processes. The method involves utilizing an assist layer immediately below the photoresist layer. The assist layer can either be directly applied to the substrate, or it can be applied to any intermediate layer(s) that may be applied to the substrate. The preferred assist layers are formed from spin-coatable, polymeric compositions. The inventive method allows reduced critical dimensions to be achieved with improved dose-to-size ratios, while improving adhesion and reducing or eliminating pattern collapse issues.