The self-similar nonlinear evolution of the multimode ablative Rayleigh-Taylor instability (ARTI) is studied numerically in both two and three dimensions. It is shown that the nonlinear multimode bubble-front penetration follows the α_{b}A_{T}(∫sqrt[g]dt)^{2} scaling law with α_{b} dependent on the initial conditions and ablation velocity. The value of α_{b} is determined by the bubble competition theory, indicating that mass ablation reduces α_{b} with respect to the classical value for the same initial perturbation amplitude. It is also shown that ablation-driven vorticity accelerates the bubble velocity and prevents the transition from the bubble competition to the bubble merger regime at large initial amplitudes leading to higher α_{b} than in the classical case. Because of the dependence of α_{b} on initial perturbation and vorticity generation, ablative stabilization of the nonlinear ARTI is not as effective as previously anticipated for large initial perturbations.