Density functional theory (DFT) and tight binding (TB) models have been used to study systems containing single-walled carbon nanotubes (SWNTs) and metal clusters that are of relevance to SWNT growth and regrowth. In particular, TB-based Monte Carlo (TBMC) simulations at 1000 or 1500 K show that Ni atoms that are initially on the surface of the SWNT or that are clustered near the SWNT end diffuse to the nanotube end so that virtually none of the Ni atoms are located inside the nanotube. This occurs, in part, due to the lowering of the Ni atom energies when they retract from the SWNT to the interior of the cluster. Aggregation of the atoms at the SWNT end does not change the chirality within the simulation time, which supports the application of SWNT regrowth (seeded growth) as a potential route for chirality-controlled SWNT production. DFT-based geometry optimisation and direct dynamics at 2000 K show that Cr and Mo atoms in Cr5Co50 and Mo5Co50 clusters prefer to be distributed in the interior of the clusters. Extension of these calculations should deepen our understanding of the role of the various alloy components in SWNT growth.