Deep convective system maximum areal extent is driven by the stratiform anvil area since system convective area fractions are much less than unity when systems reach peak size. It is important to understand the processes that drive system size given the impact large systems have on rainfall and since anvils may strongly impact high cloud feedbacks. Using satellite diabatic heating and convective-stratiform information mapped to convective systems, composite analyses suggest that system maximum sizes occur at the temporal mid-point of system lifecycles with both maximum size and duration correlating with peak heating above the melting level. However, variations in system growth rates exist, with the overall smooth composites emerging as the average of highly variable system trajectories. Thus, this study focuses on understanding convective system growth rates on short (30-minute) timescales via development of a simple analytical source - sink model that predicts system area changes. Growth occurs when detrained convective mass (inferred from the vertical gradient of diabatic heating and temperature lapse rates) and/or generation of convective area exceeds a sink term whose magnitude is proportional to the current cloud shield size. The model works well for systems over land and ocean, and for systems characterized by varying degrees of convective organization and duration (1.5 - 35 hr, with correlations often >0.8 across lifetime bins). The model may serve as a useful foundation for improved understanding of processes driving changes in tropics-wide convective system cloud shields, and further supports conceptual development and evaluation of prognostic climate model stratiform anvil area parameterizations.