  We present intermediate resolution ($\sim3$ \AA ) spectra of the Ly$\alpha$
emission from 15 high redshift radio galaxies ($z>2$). Together with previously
published spectra we analyze data for a sample of 18 objects.
  In 11 of the 18 radio galaxies we find deep troughs in the Ly$\alpha$
emission profile, which we interpret as H\,{\sc i} absorption with column
densities in the range $10^{18}$--$10^{19.5}$ cm$^{-2}$. Since in most cases
the Ly$\alpha$ emission is absorbed over its entire spatial extent (up to 50
kpc), the absorbers must have a covering fraction close to unity. Under
plausible assumptions for the temperature and density of the absorbing gas this
implies that the absorbing material must consist of $\sim 10^{12}$ clouds of
typical size $\sim 0.03$ pc with a total mass of $\sim 10^8$ M$_{\odot}$.
  Our observations show that strong H\,{\sc i} absorption occurs in $>60$\% of
the high redshift radio galaxies, while from the statistics of quasar
absorption lines there is only a 2\% probability of such a strong H\,{\sc i}
absorption line falling by chance in the small redshift interval of the
Ly$\alpha$ emission line. These absorbers are therefore most likely to be
physically associated with the galaxy hosting the radio source or its direct
environment.
  There are strong correlations between the properties of the Ly$\alpha$
emission of the galaxies and the size of the associated radio source: (i) Of
the smaller ($<50$ kpc) radio galaxies 9 out of 10 have strong associated
H\,{\sc i} absorption, whereas only 2 of the 8 larger ($>50$ kpc) radio
galaxies show such strong absorption. (ii) Larger radio sources tend to have
larger Ly$\alpha$ emission regions and (iii) a smaller Ly$\alpha$ velocity
