This paper presents a new power conversion method that can achieve both high efficiency and high power density by obviating the need for an area-consuming flying capacitor and replacing it with a flying digital load. The proposed flying-domain (FD) power conversion concept enables higher conversion efficiency than a conventional switched-capacitor converter by reducing charge-sharing and bottom-plate parasitic losses, while also enabling higher power density by eliminating the area occupied by the flying passive itself. This paper presents state-space analysis that shows that the proposed FD concept is well posed and reaches a valid steady state, while also presenting experimental results of several FD converters implemented in 180 nm SOI. With no flying passives, the fabricated FD converter achieves a peak efficiency of 99.2%, delivers up to 11.8 W/mm2 (2.3 W/mm2 with decoupling) at 91.7% efficiency, and can directly power a cofabricated Cortex M0 processor that communicates via flying I/O level shifters.