We find the key behind the existence traits of asymptotic saturated nonlinear optical solitons in the emergence of linear wave segments. These traits, produced by the progressive relegation of nonlinear dynamics to wave tails, allow a direct and versatile analytical prediction of self-trapping existence conditions and simple soliton scaling laws, which we confirm experimentally in saturated-Kerr self-trapping observed in photorefractives. This approach provides the means to correctly evaluate beam tails in the saturated regime, which is instrumental in the prediction of soliton interaction forces. (C) 2003 Optical Society of America.