  We use a sample of 27 GRBs at redshift $z=2-6$ to probe the outflows in their
respective host galaxies ($\mathrm{log(M_*/M_{\odot})}~\sim~9-11$) and search
for possible relations between the outflow properties and those of the host
galaxies such as $\mathrm{M_*}$, SFR, and specific SFR. First, we consider
three outflow properties $-$ outflow column density ($\mathrm{N_{out}}$),
maximum outflow velocity ($\mathrm{V_{max}}$), and normalized maximum velocity
($\mathrm{V_{norm}}$ = $\mathrm{V_{max}/V_{circ, halo}}$, where
$\mathrm{V_{circ,halo}}$ is the halo circular velocity). We observe clear
trends of $\mathrm{N_{out}}$ and $\mathrm{V_{max}}$ with increasing SFR in
high-ion-traced outflows, with a stronger ($>~3\sigma$) $\mathrm{V_{max}}-$SFR
correlation. We find that the estimated mass outflow rate and momentum flux of
the high-ion outflows scale with SFR and can be supported by the momentum
imparted by star formation (supernovae and stellar winds). The kinematic
correlations of high-ion-traced outflows with SFR are similar to those observed
for star-forming galaxies at low redshifts.
  The correlations with SFR are weaker in low-ions. This, along with the lower
detection fraction in low-ions, indicates that the outflow is primarily
high-ion dominated. We also observe a strong ($>~3\sigma$) trend of normalized
velocity ($\mathrm{V_{norm}}$) decreasing with halo mass and increasing with
sSFR, suggesting that outflows from low-mass halos and high-sSFR galaxies are
most likely to escape and enrich the outer CGM and IGM with metals. By
comparing the CGM-GRB stacks with those of starbursts at $z\sim2$ and
$z\sim0.1$, we find that over a broad redshift range, the outflow strength
strongly depends on the main-sequence offset at the respective redshifts rather
than simply the SFR.
