The question of how the texture and structure of carbon nanofilaments (CNTs) are determined during growth is addressed via their preparation using the vapour phase method over Ni–Cu–Mg–Al catalysts. The CNTs formed and the related catalyst particles were investigated by high resolution transmission electron microscopy, electron diffraction, and X-ray energy dispersive spectroscopy. The nanofilament features were found to directly relate to the catalyst particle size and morphologies, which in turn depend on both the Ni/Cu ratio in the Ni–Cu alloy that forms the catalyst particles and the route by which they were prepared. The extent and orientation of graphenes within the carbon nanofilaments were found to be controlled by the extent of the related catalyst crystal faces and the angle value between the latter. It is proposed that energetics of graphenes, basically involving the ratio of the edge over the core carbon atoms, the energetic cost of heterocycles (pentagon), and that of the stress induced by the strain at graphene bending sites, determine whether the carbon nanofilaments would actually grow as nanotubes (i.e., hollow) with the dual “herringbone–bamboo” texture, or as nanofibres (i.e., not hollow) with either the “herringbone” texture or the platelet texture. Only the latter allowed the genuine graphite (3D periodicity) structure to develop, while the other nanofilament types could merely adopt the turbostratic structure. Meanwhile, it was demonstrated that the herringbone nanotubes and nanofibres here prepared are of “cup-stack” rather than “single helix” type.