© 2016 American Physical Society. We investigate spatial adiabatic passage of a Bose-Einstein condensate in a triple-well potential within the three-mode approximation. By rewriting the dynamics in the so-called time-dependent dark-dressed basis, we analytically derive the optimal conditions for the nonlinear parameter and the on-site energies of each well to achieve a highly efficient condensate transport. We show that the nonlinearity yields a high-efficiency plateau for the condensate transport as a function of the on-site energy difference between the outermost wells, favoring the robustness of the transport. We also analyze the case of different nonlinearities in each well, which, for certain parameter values, leads to an increase of the width of this plateau.