There is a demand for the manufacture of two-dimensional (2D) materials with high-quality single crystals of large size. Usually, epitaxial growth is considered the method of choice 1 in preparing single-crystalline thin films, but it requires single-crystal substrates for deposition. Here we present a different approach and report the synthesis of single-crystal-like monolayer graphene films on polycrystalline substrates. The technological realization of the proposed method resembles the Czochralski process and is based on the evolutionary selection 2 approach, which is now realized in 2D geometry. The method relies on 'self-selection' of the fastest-growing domain orientation, which eventually overwhelms the slower-growing domains and yields a single-crystal continuous 2D film. Here we have used it to synthesize foot-long graphene films at rates up to 2.5 cm h-1 that possess the quality of a single crystal. We anticipate that the proposed approach could be readily adopted for the synthesis of other 2D materials and heterostructures.