Density-functional ab initio molecular dynamics (AIMD) simulations are carried out to determine Cu adatom and admolecule transport properties as a function of temperature, as well as atomistic processes leading to formation of Cu/TiN(0 0 1) islands at 350 K. At very low temperatures T ≤ 200 K, Cu adatoms (Cuad) migrate among favored fourfold-hollow surface sites by passing across atop-Ti metastable positions. For increasing temperatures, however, Cuad transport becomes progressively more isotropic, and switches continuously from normal- to super-diffusive with mean-square displacement dependencies on time that alternate between linear and exponential. Despite that, the Cuad diffusivity D can be expressed by a fairly Arrhenius-like behavior D(T) = 8.26(×2±1) × 10−4 cm2 s−1exp[(−0.04 ± 0.01 eV)/(kBT)] over the entire investigated temperature range (100 ≤ T ≤ 1000 K). AIMD simulations also reveal that the condensation of Cu adatoms into Cux>1 adspecies is kinetically hindered by long-range (>5.5 Å) adatom/adatom repulsion. During Cu island nucleation, all Cu atoms occupy atop-N positions indicating favored Cu(0 0 1)/TiN(0 0 1) epitaxial growth. Nevertheless, Cu agglomerates formed by five, or more, atoms tend to arrange in 3D structures, which maximize intracluster bonds while minimizing film/substrate interactions. Results here presented provide insights for understanding the properties of weakly-interacting metal/substrate interface systems in general.