The present invention is directed to fibers of epitaxially grown single-wall carbon nanotubes (SWNTs) and methods of making same. Such methods generally comprise the steps of: (a) providing a spun SWNT fiber; (b) cutting the fiber substantially perpendicular to the fiber axis to yield a cut fiber; (c) etching the cut fiber at its end with a plasma to yield an etched cut fiber; (d) depositing metal catalyst on the etched cut fiber end to form a continuous SWNT fiber precursor; and (e) introducing feedstock gases under SWNT growth conditions to grow the continuous SWNT fiber precursor into a continuous SWNT fiber.