One-point measurements made with a phase Doppler anemometer allow us to measure droplets' velocity (two components) and diameter in a stationary spray produced by the discharge of pressurized water through a sharp-edged nozzle. This two-phase flow, first driven by the dense atomized liquid, reaches, at sufficient distance from the injector, a state where the motion of the dispersed phase (the droplets) is controlled by the continuous phase (the air), and the spray can be considered as fully developed. This transition can be recognized by five different criteria. (1) The first is based on the droplet mean axial velocity. (2) The second arises from the measurement of the air entrainment around the spray. (3) The profiles of the dimensionless fluctuations of tire drop axial velocity represent the third criterion. (4) The fourth is related to the mean-square droplet displacement (estimated from the drops let flux profiles). (5) The last is connected with the evolution of the mixing layer thickness, based on the momentum of the droplets. We found that the transition to the fully developed regime is not reached at the same location for each class of droplet size, suggesting a selective response of the droplets to the surrounding gas flow. Tire validation of the above-proposed criteria on complementary experiments performed with two nozzles having the same geometry but different internal roughness indicates that they can be used as a practical diagnostic to identify the transition in this type of jets.