Single-crystal nanowire transistors and other nanowire-based devices could have applications in large-area and flexible electronics if conventional top-down fabrication techniques can be integrated with high-precision bottom-up nanowire assembly. Here, we extend dielectrophoretic nanowire assembly to achieve a 98.5% yield of single nanowires assembled over 16,000 patterned electrode sites with submicrometre alignment precision. The balancing of surface, hydrodynamic and dielectrophoretic forces makes the self-assembly process controllable, and a hydrodynamic force component makes it self-limiting. Our approach represents a methodology to quantify nanowire assembly, and makes single nanowire assembly possible over an area limited only by the ability to reproduce process conditions uniformly.