One of the biggest limitations of conventional carbon nanotube device fabrication techniques is the inability to scale up the processes to fabricate a large number of devices on a single chip. In this report, we demonstrate the directed and precise assembly of single-nanotube devices with an integration density of several million devices per square centimeter, using a novel aspect of nanotube dielectrophoresis. We show that the dielectrophoretic force fields change incisively as nanotubes assemble into the contact areas, leading to a reproducible directed assembly which is self-limiting in forming single-tube devices. Their functionality has been tested by random sampling of device characteristics using microprobes.