A novel strategy is proposed for the topologically controlled synthesis of extended graphenic sheets by additively reacting carbon into a pre-existing graphene sheet which is on top of a templating substrate. This concept is implemented and demonstrated using chemical vapor deposition (CVD). Novel morphological features observed in this study suggest unusual aspects of the CVD growth process. CVD results demonstrate the basic soundness of the synthesis strategy but highlight the sensitivity of the process to certain types of disruption and the need for alternative forms of embodiment.