The direct observation of single crystal graphene growth and its shape evolution is of fundamental importance to the understanding of graphene growth physicochemical mechanisms and the achievement of wafer-scale single crystalline graphene. Here we demonstrate the controlled formation of single crystal graphene with varying shapes, and directly observe the shape evolution of single crystal graphene by developing a localized-heating and rapid-quenching chemical vapor deposition (CVD) system based on electromagnetic induction heating. Importantly, rational control of circular, hexagonal, and dendritic single crystalline graphene domains can be readily obtained for the first time by changing the growth condition. Systematic studies suggest that the graphene nucleation only occurs during the initial stage, while the domain density is independent of the growth temperatures due to the surface-limiting effect. In addition, the direct observation of graphene domain shape evolution is employed for the identification of competing growth mechanisms including diffusion-limited, attachment-limited, and detachment-limited processes. Our study not only provides a novel method for morphology-controlled graphene synthesis, but also offers fundamental insights into the kinetics of single crystal graphene growth.C hemical vapor deposition (CVD) has enabled the growth of single layer graphene over large area through the optimization of synthesis conditions 1-3 , including hydrogen and carbon precursors flow rates 4-6 , surface oxygen 7 , substrate 8,9 , temperature 10 , and pressure 11 . In order to achieve large size and high-quality single crystal graphene, a fundamental understanding of precise mechanisms that governs the formation of graphene domains is necessary. Much effort has been placed on the investigation of graphene growth kinetics by using carbon isotope labeling technique 7,12,13 , or the empirical parameters-controlled methods based on the nucleation and growth theory 14 . It has been widely accepted that the graphene growing process mainly involves surface catalytic reaction for catalyst with low-carbon solubility 1,13 . In this case, graphene nucleation on catalyst surface is one of the critical steps in the growth process. Various factors affect the initiation of graphene nucleation process, including the type or surface morphology of catalyst 15,16 , carbon source 17 , carbon segregation from metalcarbon melts 18 , and parameters in CVD growth 2,19,20 . In general, nucleation densities on polycrystal Cu substrates are nonuniform, representing a key problem in high quality graphene film synthesis. Recently it has been found that uniform nucleation distribution, low nucleation density and highly ordered single crystal graphene films can be obtained by using liquid Cu film as catalytic, which is possibly due to the elimination of Cu grain boundaries 21,22 . However, the direct insight of single crystal graphene growth and its corresponding domain shape evolution during the growth process are still lacking. The chall...