Low-temperature (∼600 °C), scalable chemical vapor deposition of high-quality, uniform monolayer graphene is demonstrated with a mapped Raman 2D/G ratio of >3.2, D/G ratio ≤0.08, and carrier mobilities of ≥3000 cm(2) V(-1) s(-1) on SiO(2) support. A kinetic growth model for graphene CVD based on flux balances is established, which is well supported by a systematic study of Ni-based polycrystalline catalysts. A finite carbon solubility of the catalyst is thereby a key advantage, as it allows the catalyst bulk to act as a mediating carbon sink while optimized graphene growth occurs by only locally saturating the catalyst surface with carbon. This also enables a route to the controlled formation of Bernal stacked bi- and few-layered graphene. The model is relevant to all catalyst materials and can readily serve as a general process rationale for optimized graphene CVD.