  We develop a count-in-cells approach to the distribution of ultraviolet
background fluctuations that includes source clustering. We demonstrate that an
exact expression can be obtained if the clustering of ionizing sources follows
the hierarchical ansatz. In this case, the intensity distribution depends
solely on their 2-point correlation function. We show that the void scaling
function of high redshift mock quasars is consistent with the Negative Binomial
form, before applying our formalism to the description of HeII-ionizing
fluctuations at the end of helium reionization. The model inputs are the
observed quasar luminosity function and 2-point correlation at redshift $z\sim
3$. We find that, for an (comoving) attenuation length $\lesssim $ 55 Mpc,
quasar clustering contributes less than 30% of the variance of intensity
fluctuations so long as the quasar correlation length does not exceed 15 Mpc.
We investigate also the dependence of the intensity distribution on the
large-scale environment. Differences in the mean HeII-ionizing intensity
between low- and high-density regions could be a factor of few if the sources
are highly clustered. An accurate description of quasar demographics and their
correlation with strong absorption systems is required to make more precise
predictions.
