We study the Kondo alloy model on a square lattice using dynamical mean-field theory for Kondo substitution and disorder effects, together with static mean-field approximations. We computed and analyzed photoemission properties as a function of electronic filling n c , Kondo impurity concentration x, and strength of Kondo temperature T K. We provide a complete description of the angle resolved photoemission spectroscopy (ARPES) signals expected in the paramagnetic (PM) Kondo phases. By analyzing the Fermi surface (FS), we observe the Lifshitz-like transition predicted previously for strong T K at x = n c and we discuss the evolution of the dispersion from the dense coherent to the dilute Kondo regimes. At smaller T K, we find that this transition marking the breakdown of coherence at x = n c becomes a crossover. However, we identify another transition at a smaller concentration x ⋆ where the effective mass continuously vanishes. x ⋆ separates the one-branch and the two-branches ARPES dispersions characterizing respectively dilute and dense Kondo PM regimes. The x − T K phase diagrams are also described, suggesting that the transition at x ⋆ might be experimentally observable since magnetically ordered phases are stabilized at much lower T K. FS reconstructions in antiferromagnetic and ferromagnetic phases are also discussed.