We study the evolution of a system of dropwise aggregates suspended in a macroscopically homogeneous metastable colloid with account of both the reduction in metastability (the decrease in the parent colloid supersaturation) and the continuing initiation of new nuclei in the metastable surroundings. The growing aggregates are distributed over size and the distribution density is governed by an equation of the Fokker-Planck type with allowance for variations in the growth rate of a single aggregate. A complementary equation relates the supersaturation to the total rate of absorption of colloidal particles by the aggregates. A method of solving those equations is worked out. It permits the supersaturation and diverse characteristics of the distribution density to be found as functions of time. The former quantity is monotonously declining to zero and the dispersion of the latter one is either decreasing or increasing with time depending on the level of random fluctuations of the growth rate. If the fluctuations are absent, the evolving system of the aggregates is tending to a monodisperse one, what calls in question the validity of underlying assumptions inherent to the classical theory of Ostwald ripening.