TiN films were grown at less than or equal to 150 degrees C on polycrystalline Cu substrates, with grain sizes of 10-30 mu m, by magnetically-unbalanced reactive magnetron sputtering in mixed Ar/N-2 discharges. The applied negative substrate bias V-s and the ion/metal ratio J(i)/J(Ti) incident at the growing film (>96% of the ions were Ar+) were varied independently : V-s=0-300 V with J(i)/J(Ti)=0.4, and J(i)/J(Ti)=0.4-9 with V-s=100 V. Films grown with J(i)/J(Ti)=0.4 were polycrystalline, with average grain sizes (d) much smaller than underlying Cu grains, and underdense. Increasing V-s, at J(i)/J(Ti)=0.4, increased [d] from 10 to 20 nm and resulted in densification, although intercolumnar boundaries remained partially voided. Unbiased J(i)/J(Ti)=0.4 films were randomly oriented while biased samples grew epitaxially with the underlying grains for thicknesses up to similar to 30 nm before the growth front gradually broke down locally to initiate competitive columnar growth. In sharp contrast, TiN films grown with J(i)/J(Ti)greater than or equal to 4 and V-s=100 V were found to be dense and to grow completely epitaxially over entire Cu grains. In addition to (001) "cube-on-cube" epitaxy, more complex relationships were observed on differently oriented Cu grains in which the TiN overlayers exhibited self-organized crystallographic tilts and/or rotations in order to reduce interfacial misfit and, hence, long-range epitaxial strain. Examples are (001)(TiN)parallel to(011)(Cu) with [100](TiN)parallel to[2(1) over bar1$](Cu) and (011)(TiN)parallel to(011)(Cu) with [0(1) over bar1$](TiN)parallel to[100](Cu).