  The colour dipole multiplicity distribution is analysed for the wave function
of a heavy onium state at small $x$. Numerical results for the average
multiplicity and the effect of cutoffs on its power growth are presented. Then,
the full multiplicity distribution is analysed: the second multiplicity moment
is derived and the tail of the distribution is shown to behave as $\exp(-\log^2
n)$. These results are confirmed by a Monte Carlo simulation which also gives
the fluctuations in the spatial density of dipoles.
