We report the rapid synthesis of millimeter-long vertically-aligned carbon-nanotubes (VACNTs) by hot-filament chemical-vapor-deposition without the use of water vapor. The growth rate increased initially up to similar to 190 mu m/min but decreased thereafter resulting in the growth of up to 2.2 +/- 0.2 mm in 23 +/- 2 min. A thermodynamic model driven by a carbon-concentration gradient can account for very rapid initial growth with Arrhenius-type exponential temperature dependence. Another model devised for the quantitative elucidation of the monotonic decrease in growth-rate and quasi saturation of VACNT growth confirmed that the growth kinetics of VACNTs are controlled by the concomitant contribution of a diffusion-limited precursor supply and reaction-driven catalyst deactivation. (C) 2011 Elsevier B.V. All rights reserved.