A method of forming high germanium content silicon germanium alloy fins with controlled insulator layer recessing is provided. A silicon germanium alloy (SiGe) layer having a first germanium content is provided on a surface of an insulator layer using a first condensation process. Following the formation of a hard mask layer portion on the SiGe layer, a second condensation process is performed to convert a portion of the SiGe layer into a SiGe fin of a second germanium content that is greater than the first germanium content and other portions of the SiGe layer into a shell oxide structure located on sidewalls of the SiGe fin. After forming a fin placeholder material, a portion of each shell oxide structure is removed, while maintaining a lower portion of each shell oxide structure at the footprint of the SiGe fin.