Flat TiO$_2$ layers are deposited by magnetron sputtering on Ti/Si wafers. The TiO$_2$ surfaces are then sputter-coated with thin Au films of a nominal thickness of 0.5-10 nm that are converted by solid-state dewetting into Au nanoparticles of tuneable size and spacing; the Au nanoparticle size can be tuned over a broad range, i.e. ca. 3-200 nm. The Au-decorated TiO$_2$ surfaces enable plasmonic photo-electrochemical water splitting under visible light illumination (450-750 nm). The water splitting performance reaches a maximum for TiO$_2$ layers decorated with ~ 30 nm-sized Au particles. As expected, optical absorption measurements show a red shift of the plasmonic extinction band with increasing the Au nanoparticle size. However, the plasmonic photocurrent is found to peak at ~ 600 nm regardless of the size of the Au nanoparticles, i.e. the plasmonic photocurrent band position is size-independent. Such a remarkable observation can be ascribed to a hot electron injection cut-off effect.