The possibilities offered by catalytic γ-Al2O3 substrates are explored, and the mechanism governing graphene formation thereon is elucidated using both numerical simulations and experiments. The growth scheme offers metal-free synthesis at low temperature, grain-size customization, large-area uniformity of electrical properties, single-step preparation of graphene/dielectric structures, and readily detachable graphene. We quantify based on thermodynamic principles the activation energies associated with graphene nucleation/growth on γ-Al2O3, verifying the low physical and chemical barriers. Importantly, we derive a universal equation governing the adsorption-based synthesis of graphene over a wide range of temperatures in both catalytic and spontaneous growth regimes. Experimental results support the equation, highlighting the catalytic function of γ-Al2O3 at low temperatures. The synthesized graphene is manually incorporated as a 'graphene sticker' into an ultrafast mode-locked laser.