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 (Cu-ad) 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(x2(+/- 1)) x 10(-4) cm(2) s(-1) exp[(-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 Cu-x>1 adspecies is kinetically hindered by long-range (> 5.5 angstrom) 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. (C) 2018 Elsevier B. V. All rights reserved.