A fully nonlinear sharp-boundary model of the ablative Rayleigh-Taylor instability is derived and closed in a similar way to the self-consistent closure of the linear theory. It contains the stabilizing effect of ablation and accurately reproduces the results of 2D DRACO simulations. The single-mode saturation amplitude, bubble and spike evolutions in the nonlinear regimes, and the seeding of long-wavelength modes via mode coupling are determined and compared with the classical theory without ablation. Nonlinear stability above the linear cutoff is also predicted.