We report a method for growing rectangular InAs nanofins with deterministic length, width, and height by dielectric-templated selective-area epitaxy. These freestanding nanofins can be transferred to lay flat on a separate substrate for device fabrication. A key goal was to regain a spatial dimension for device design compared to nanowires, while retaining the benefits of bottom-up epitaxial growth. The transferred nanofins were made into devices featuring multiple contacts for Hall effect and four-terminal resistance studies, as well as a global back-gate and nanoscale local top-gates for density control. Hall studies give a 3D electron density 2.5-5 × 1017 cm-3, corresponding to an approximate surface accumulation layer density 3-6 × 1012 cm-2 that agrees well with previous studies of InAs nanowires. We obtain Hall mobilities as high as 1200 cm2/(V s), field-effect mobilities as high as 4400 cm2/(V s), and clear quantum interference structure at temperatures as high as 20 K. Our devices show excellent prospects for fabrication into more complicated devices featuring multiple ohmic contacts, local gates, and possibly other functional elements, for example, patterned superconductor contacts, that may make them attractive options for future quantum information applications.