In the current study, we have performed ab initio DFT calculations on the gradually growing 2D periodic models of capped single-wall carbon nanotubes (SW CNTs) upon their perpendicular junctions with the Ni(111) substrate, in order to understand the peculiarities of the initial stage of their growth on either smooth or nanostructured catalytic particles. Appearance of the adsorbed carbon atoms upon the substrate follows from the dissociation of CVD hydrocarbon molecules, e.g., CH4: (CH4)ads → (CH)ads+3Hads and (CH)ads → Cads+Hads. (Since the effective growth of CNTs upon Ni nanoparticles occur inside the nanopores of amorphous alumina, we have also simulated analogous surface reactions upon the θ-Al2O3(010) slabs). Association of the adsorbed carbon atoms upon the catalyst surface precedes further swelling of the (Cn)ads islands after appearance of pentagonal defects within a honeycomb sheet which are more probable upon the catalyst surface containing either defects or nanoclusters (as in the case of the nanostructured substrate). The gradual growth of the capped CNTs is considerably more effective upon the nanostructured Ni(111) substrate compared to a smooth nickel substrate (cf. values of CNT adhesion energy per boundary C atom for chiralities of either armchair-type, 4.04 vs. 2.51 eV, or zigzag-type, 4.61 vs. 2.14 eV, respectively). The electronic charge transfer from the Ni catalyst towards the CNTs has been calculated for both chiralities (> 1 e per C atom), i.e., quite strong chemical bonds are formed within the CNT/Ni(111) interconnects.