Molecular beam epitaxy of Cu on Cu(111) was studied using thermal energy He scattering, in the temperature range between 100 and 450 K. Three-dimensional growth was observed in the whole temperature range. To determine the onset of various diffusion processes, submonolayer films formed by deposition at low temperature were annealed. Annealing proceeds in two steps. The first step is interpreted as a change in island shape, the second as Ostwald-ripening. A comparison with homoepitaxy on Pt(111) and Ag(111) is made. Growth manipulation was carried out by artificially increasing the island number density via intervention in the nucleation stage of each layer. The procedures applied were temperature reduction during nucleation as well as pulsed ion bombardment. These techniques enabled the convenient growth of good quality films consisting of a large number of monolayers. Finally, the use of oxygen as a surfactant modifying the growth mode was investigated. Under some growth conditions, pre-exposure of the surface to oxygen was found to induce weak He-intensity oscillations during deposition. The quality of the films grown in this way was, however, low.