Unresolved problems associated with the production of graphene materials include the need for greater control over layer number, crystallinity, size, edge structure and spatial orientation, and a better understanding of the underlying mechanisms. Here we report a chemical vapor deposition approach that allows the direct synthesis of uniform single-layered, large-size (up to 10,000 μm(2)), spatially self-aligned, and single-crystalline hexagonal graphene flakes (HGFs) and their continuous films on liquid Cu surfaces. Employing a liquid Cu surface completely eliminates the grain boundaries in solid polycrystalline Cu, resulting in a uniform nucleation distribution and low graphene nucleation density, but also enables self-assembly of HGFs into compact and ordered structures. These HGFs show an average two-dimensional resistivity of 609 ± 200 Ω and saturation current density of 0.96 ± 0.15 mA/μm, demonstrating their good conductivity and capability for carrying high current density.