The development of topography within and erosional removal of material from an orogen exerts a primary control on its structure. We develop a model that describes the temporal development of a frontally accreting, critically growing Coulomb wedge whose topography is largely limited by bedrock fluvial incision. We present general results for arbitrary initial critical wedge geometries and investigate the temporal development of a critical wedge with no initial topography. Increasing rock erodibility and/or precipitation, decreasing mass flux accreting to the wedge front, increasing wedge sole-out depth, decreasing wedge and basal decollement overpressure, and increasing basal decollement friction lead to narrow wedges. Large power law exponent values cause the wedge geometry to quickly reach a condition in which all material accreted to the front of the wedge is removed by erosion. We apply our model to the Aconcagua fold-and-thrust belt in the central Andes of Argentina where wedge development over time is well constrained. We solve for the erosional coefficient K that is required to recreate the field-constrained wedge growth history, and these values are within the range of independently determined values in analogous rock types. Using qualitative observations of rock erodibilities within the wedge, we speculate that power law exponents of 1/3 ≤ m ≤ 0.4 and 2/3 ≤ n ≤ 1 characterize the erosional growth of the Aconcagua fold-and-thrust belt. This general model may be used to understand the development of mountain belts where orogenic wedges grow as they deform at their Coulomb failure limit.