A (1+1)-dimensional model is studied numerically to evidence the build up mechanisms of photorefractive solitons, from the characteristic carrier recombination time, through the quasi-steady-state soliton, to the screening soliton. Three different build up regimes are evidenced and their domain of existence are computed. The transient quasi-steady-state soliton is shown to be characterized by two constants: its normalized width and its normalized build up time response multiplied by its peak intensity over dark irradiance. This latter assertion allows us to predict the photorefractive soliton response time for various optical powers. It is thus compared to existing experimental results.