Breakthroughs extending nanostructure engineering beyond what is possible with current fabrication techniques will be crucial for enabling next-generation nanotechnologies. Nanoepitaxy of strain-engineered bent nanowire heterostructures presents a promising platform for realizing the bottom-up and scalable fabrication of nanowire devices. The synthesis of these structures requires the selective asymmetric deposition of lattice-mismatched shells�a complex growth process that is not well understood. We present the nanoepitaxial growth of GaAs−InP core−shell bent nanowires and connecting nanowire pairs to form nanowire arches. The out-of-plane geometry and dual substrate connection of nanowire arches make these nanostructures highly promising for sensor-based applications. Compositional analysis of nanowire cross sections reveals the critical role of adatom diffusion in the nanoepitaxial growth process, which leads to two distinct growth regimes: indium-diffusion-limited growth and phosphorus-limited growth. The highly controllable phosphorus-limited growth mode is employed to synthesize connected nanowire pairs and quantify the role of flux shadowing on the shell growth process. Nanowires connected with shadowing are intimately fused, with the majority of shell growth forming near the interface of the two nanowires. These results provide important insight into 3D nanoepitaxy and enable possibilities for nanowire device fabrication.