Vertically aligned carbon nanotubes (CNTs) are an important technological system, as well as a fascinating system for studying basic principles of nanomaterials synthesis; yet despite continuing efforts for the past decade many important questions about this process remain largely unexplained. We present a series of parametric ethylene chemical vapor deposition growth studies in a "hot-wall" reactor using ultrapure process gases that reveal the fundamental kinetics of the CNT growth. Our data show that the growth rate is proportional to the concentration of the carbon feedstock and monotonically decreases with the concentration of hydrogen gas and that the most important parameter determining the rate of the CNT growth is the production rate of active carbon precursor in the gas phase reaction. The growth termination times obtained with the purified gas mixtures were strikingly insensitive to variations in both hydrogen and ethylene pressures ruling out the carbon encapsulation of the catalyst as the main process termination cause.