The cluster size distribution Ck(t) in aggregation and coagulation phenomena for large cluster sizes k and large times t approaches a scaling form of self-preserving spectrum ck(t)'~ s -2 ~o(k/s), where s(t) is the mean cluster size. In a mean field approach the scaling form ~o(x) is described by a nonlinear integrodifferential equation, obtained from Smoluchowski's coagulation equation. To verify some theoretical predictions and to provide quantitative information on the scaling form we develop a fixed point method to determine numerical solutions of this equation for aggregation rate constants K(x, y) = x~y ~ + y~x ~ with a >/3 and fl < 0 (class III models), where ~o(x) is bell-shaped, and we study the crossover to class II models (/3 = 0), where ~o(x) ~ x -~ as x ~ 0, and calculate the exponent r.