Laser-assisted chemical vapour deposition (CVD) growth is an attractive mask-less process for growing locally aligned carbon nanotubes (CNTs) in selected places on temperature sensitive substrates. The nature of the localized process results in fast carbon nanotube growth with high experimental throughput. Here, we report on detailed investigation of growth kinetics related to physical and chemical process characteristics. Specifically, the growth kinetics is investigated by monitoring the dynamical changes of reflected laser beam intensity during growth. Benefiting from the fast growth and high experimental throughput, we investigate a wide range of experimental conditions and propose several growth regimes. Rate-limiting steps are determined using rate equations linked to the proposed growth regimes, which are further characterized by Raman spectroscopy and Scanning Electron Microscopy (SEM), therefore directly linking growth regimes to the structural quality of the CNTs. Activation energies for the different regimes are found in the range of 0.3 – 0.8 eV.