How cell specification can be controlled in a reproducible manner is a fundamental question in developmental biology. In ascidians, a group of invertebrate chordates, geometry plays a key role in achieving this control. Here, we use mathematical modeling to demonstrate that geometry dictates the neural-epidermal cell fate choice in the 32-cell stage ascidian embryo by a two-step process involving first the modulation of ERK signaling and second, the expression of the neural marker gene, Otx. The model describes signal transduction by the ERK pathway that is stimulated by FGF and attenuated by ephrin, and ERK-mediated control of Otx gene expression, which involves both an activator and a repressor of ETS-family transcription factors. Considering the measured area of cell surface contacts with FGF- or ephrin-expressing cells as inputs, the solutions of the model reproduce the experimental observations about ERK activation and Otx expression in the different cells under normal and perturbed conditions. Sensitivity analyses and computations of Hill coefficients allow us to quantify the robustness of the specification mechanism controlled by cell surface area and to identify the respective role played by each signaling input. Simulations also predict in which conditions the dual control of gene expression by an activator and a repressor that are both under the control of ERK can induce a robust ON/OFF control of neural fate induction.