  We present 3D resonant radiative transfer simulations of the spatial and
spectral diffusion of the Lya radiation from a central source in the host
galaxies of high column density absorption systems at z ~ 3. The radiative
transfer simulations are based on a suite of cosmological galaxy formation
simulations that reproduce a wide range of observed properties of damped Lya
absorption systems. The Lya emission is predicted to be spatially extended up
to several arcsec, and the spectral width of the Lya emission is broadened to
several hundred (in some case more than thousand) km/s. The distribution and
the dynamical state of the gas in the simulated galaxies is complex, the latter
with significant contributions from rotation and both in- and out-flows. The
emerging Lya radiation extends to gas with column densities of N_HI ~ 10^{18}
cm^{-2} and its spectral shape varies strongly with viewing angle. The strong
dependence on the central \hi column density and the HI velocity field suggests
that the Lya emission will also vary strongly with time on timescales of a few
dynamical times of the central region. Such variations with time should be
especially pronounced at times where the host galaxy undergoes a major merger
and/or starburst. Depending on the pre-dominance of in- or out-flow along a
given sightline and the central column density, the spectra show prominent blue
peaks, red peaks or double-peaked profiles. Both spatial distribution and
spectral shape are very sensitive to details of the galactic wind
implementation. Stronger galactic winds result in more spatially extended Lya
emission and - somewhat counterintuitively - a narrower spectral distribution.
