  Cosmic reionization progresses as HII regions form around sources of ionizing
radiation. Their average size grows continuously until they percolate and
complete reionization. We demonstrate how this typical growth can be calculated
around the largest, biased sources of UV emission, such as quasars, by further
developing an analytical model based on the excursion set formalism. This
approach allows us to calculate the sizes and growth of the HII regions created
by the progenitors of any dark matter halo of given mass and redshift with a
minimum of free parameters. Statistical variations in the size of these
pre-existing HII regions are an additional source of uncertainty in the
determination of very high redshift quasar properties from their observed HII
region sizes. We use this model to demonstrate that the transmission gaps seen
in very high redshift quasars can be understood from the radiation of only
their progenitors and associated clustered small galaxies. The fit sets a lower
limit on the redshift of overlap at z = 5.8 +/- 0.1. This interpretation makes
the transmission gaps independent of the age of the quasars observed. If this
interpretation were correct it would raise the prospects of using radio
interferometers currently under construction to detect the epoch of
reionization.
