  Domain size distribution in phase separating binary Bose--Einstein
condensates is studied theoretically by numerically solving the
Gross--Pitaevskii equations at zero temperature. We show that the size
distribution in the domain patterns arising from the dynamic instability obeys
a power law in a scaling regime according to the dynamic scaling analysis based
on the percolation theory. The scaling behavior is kept during the relaxation
development until the characteristic domain size becomes comparable to the
linear size of the system, consistent with the dynamic scaling hypothesis of
the phase-ordering kinetics. Our numerical experiments indicate the existence
of a different scaling regime in the size distribution function, which can be
caused by the so-called coreless vortices.
