  To investigate the presence of small scale structure in the spatial
distribution of H2 molecules we have undertaken repeated FUSE UV observations
of the runaway O9.5V star, HD34078. In this paper we present five spectra
obtained between January 2000 and October 2002. These observations reveal an
unexpectedly large amount of highly excited H2. Column densities for H2 levels
from (v = 0, J = 0) up to (v = 0, J = 11) and for several v = 1 and v = 2
levels are determined. These results are interpreted in the frame of a model
involving essentially two components: i) a foreground cloud (unaffected by
HD34078) responsible for the H2 (J = 0, 1), CI, CH, CH+ and CO absorptions; ii)
a dense layer of gas (n = 10E4 cm-3) close to the O star and strongly
illuminated by its UV flux which accounts for the presence of highly excited
H2. Our model successfully reproduces the H2 excitation, the CI fine-structure
level populations as well as the CH, CH+ and CO column densities. We also
examine the time variability of H2 absorption lines tracing each of these two
components. From the stability of the J = 0, 1 and 2 damped H2 profiles we
infer a 3 sigma upper limit on column density variations Delta(N(H2))/N(H2) of
5% over scales ranging from 5 to 50 AU. This result clearly rules out any
pronounced ubiquitous small scale "density" structure of the kind apparently
seen in HI. The lines from highly excited gas are also quite stable (equivalent
to Delta(N)/N <= 30%) indicating i) that the ambient gas through which HD34078
is moving is relatively uniform and ii) that the gas flow along the shocked
layer is not subject to marked instabilities
