We report here a self-organized electroless deposition of copper in an ultrathin layer CuSO4 of electrolyte. Microscopically the branching rate of the copper deposits is significantly decreased, forming an array of smooth polycrystalline filaments. Compared with a conventional electrodeposition system, no macroscopic electric field is involved and the thickness of the electrolyte layer is greatly decreased. Therefore the electroless deposition takes place in a nearly ideal, two-dimensional diffusion-limited environment. We suggest that restriction of the thickness of the electrolyte film is responsible for the generation of smoother branches of the electrodeposits. Our data also show that even in a diffusion-limited scenario the aggregate morphology is not necessarily very ramified and fractal-like.