  We have obtained spatially resolved spectra of the z=3.911 triply imaged QSO
APM08279+5255 using the Space Telescope Imaging Spectrograph (STIS) on board
the Hubble Space Telescope (HST). We study the line of sight equivalent width
(EW) differences and velocity shear of high and low ionization absorbers
(including a damped Lyman alpha [DLA] system identified in a spatially
unresolved ground based spectrum) in the three lines of sight. We find that
high ionization systems (primarily CIV absorbers) do not exhibit strong EW
variations on scales <0.4 kpc; their fractional EW differences are typically
less than 30%. When combined with previous work on other QSO pairs, we find
that the fractional variation increases steadily with separation out to at
least ~100 kpc. Conversely, low ionization systems (primarily MgII absorbers)
show strong variations (often > 80%) over kpc scales. A minimum radius for
strong (EW > 0.3 A) MgII systems of > 1.4 kpc is inferred from absorption
coincidences in all lines of sight. For weak MgII absorbers (EW < 0.3 A), a
maximum likelihood analysis indicates a most probable coherence scale of 2.0
kpc for a uniform spherical geometry, with 95% confidence limits ranging
between 1.5 and 4.4 kpc. Finally, for systems with weak absorption that can be
confidently converted to column densities, we find constant N(CIV)/N(SiIV)
across the three lines of sight. Similarly, the [Al/Fe] ratios in the z = 2.974
DLA are consistent with solar relative abundances over a transverse distance of
\~0.35 kpc. (abrdiged)
