  A selection problem that appears in the Lifshitz-Slyozov (LS) theory of
Ostwald ripening is reexamined. The problem concerns selection of a
self-similar distribution function (DF) of the minority domains with respect to
their sizes from a whole one-parameter family of solutions. A strong selection
rule is found via an account of fluctuations. Fluctuations produce an infinite
tail in the DF and drive the DF towards the "limiting solution" of LS or its
analogs for other growth mechanisms.
