There is a demand for manufacturing 2D materials with the ultimate quality of single crystals and arbitrary size. Usually, epitaxial growth is considered the method of choice1 in preparing single crystalline thin films but it in turn requires single crystal substrates for deposition. Here we present a different approach and report synthesis of single-crystal-like monolayer graphene films on polycrystalline substrates. Technological realization of the proposed method resembles Czochralski process and is based on the evolutionary selection2 approach which is now realized in the 2D geometry. The method relies on “self-selection” of the fastest growing domain orientation that 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 with rates up to 2.5 cm/h which possess the quality of single crystal. We anticipate that the proposed approach can be readily adopted for synthesis of other 2D materials and heterostructures.