In this paper, large-mode-area, double-cladding, rare-earth-doped photonic crystal fibers are investigated in order to understand how the refractive index distribution and the mode competition given by the amplification can assure single-mode propagation. Fibers with different core diameters, i.e., 35, 60 and 100 µm, are considered. The analysis of the mode effective index, overlap, effective area, gain, and power evolution along the doped fiber provides clear guidelines on the fiber physical characteristics to be matched in the fabrication process to obtain a truly or effectively single-mode output beam.