  The HII regions around quasars and galaxies at redshifts beyond the epoch of
reionisation will provide prime targets for upcoming 21cm campaigns using a new
generation of low-frequency radio observatories. Here we show that the
boundaries of these HII regions will not be sharp. Rather, the clustering of
sources near massive galaxies results in a neutral fraction that rises
gradually towards large radii from an interior value near zero. A neutral
fraction corresponding to the global background value is typically reached at a
distance of 2-5 times the radius of the HII region around the central massive
galaxy.
