Combination of an oxide semiconductor with a highly conductive nanocarbon framework (such as graphene or carbon nanotubes) is an attractive avenue to assemble efficient photoelectrodes for solar fuel generation. To fully exploit the possible synergies of the hybrid formation, however, precise knowledge of these systems is required to allow rational design and morphological engineering. In this paper, we present the controlled electrochemical deposition of nanocrystalline p-Cu2O on the surface of different graphene substrates. The developed synthetic protocol allowed tuning of the morphological features of the hybrids as deduced from electron microscopy. (Photo)electrochemical measurements (including photovoltammetry, electrochemical impedance spectroscopy, photocurrent transient analysis) demonstrated better performance for the 2D graphene containing photoelectrodes, compared to the bare Cu2O films, the enhanced performance being rooted in suppressed charge carrier recombination. To elucidate the precise role of graphene, comparative studies were performed with carbon nanotube (CNT) films and 3D graphene foams. These studies revealed, after allowing for the effect of increased surface area, that the 3D graphene substrate outperformed the other two nanocarbons. Its interconnected structure facilitated effective charge separation and transport, leading to better harvesting of the generated photoelectrons. These hybrid assemblies are shown to be potentially attractive candidates in photoelectrochemical energy conversion schemes, namely CO2 reduction.