*To whom correspondence should be addressed.

labeling ABSTRACT. Using ethanol as the carbon source, self-limiting growth of AB-stacked bilayer graphene (BLG) has been achieved on Cu via an equilibrium chemical vapor deposition (CVD) process. We found that during this alcohol catalytic (AC-) CVD, a source-gas pressure range exists to break the self-limitation of monolayer graphene on Cu, and at a certain equilibrium state it prefers to form uniform BLG with a high surface coverage of ~94 % and AB-stacking ratio of nearly 100%. More importantly, once the BLG is completed, this growth shows a self-limiting manner and an extended ethanol flow time does not result in additional layers. We investigate the mechanism of this equilibrium BLG growth using the isotopically labeled 13C-ethanol and selective surface aryl functionalization, and results reveal that during the equilibrium ACCVD process, a continuous substitution of graphene flakes occurs to the as-formed graphene, and the BLG growth follows a layer-by-layer epitaxy mechanism. These phenomena are significantly in contrast to those observed for previously reported BLG growth using methane as precursor.