  This paper presents deep K-band spectroscopic observations of galaxies at
z=3-4 with composite photometric rest-frame Hb+[OIII] equivalent widths
EW_0>600A, comparable to the EW of galaxies observed during the epoch of
reionisation (EoR, z>6). The typical spectroscopic [OIII] EW_0 and stellar mass
of our targets is ~ 700A and log(M_star/M_sun)=8.98. By stacking the [OIII]
emission profiles, we find evidence of a weak broad component with
F_broad/F_narrow ~ 0.2 and velocity width sigma_{broad} ~ 170 km/s. The
strength and velocity width of the broad component does not change
significantly with stellar mass and [OIII] EW_0 of the stacked sample. Assuming
similar broad component profiles for [OIII] and Halpha emission, we estimate a
mass loading factor ~0.2, similar to low stellar mass galaxies at z>1 even if
the star formation rates of our sample is 10 times higher. We hypothesize that
either the multi-phase nature of supernovae driven outflows or the suppression
of winds in the extreme star-forming regime is responsible for the weak
signature of outflows in the EoR analogues.
