  We present results on the properties of extreme gas outflows in massive ($\rm
M_* \sim$10$^{11} \ \rm M_{\odot}$), compact, starburst ($\rm SFR \sim$$200 \,
\rm M_{\odot} \ yr^{-1}$) galaxies at z = $0.4-0.7$ with very high star
formation surface densities ($\rm \Sigma_{SFR} \sim$$2000 \,\rm M_{\odot} \
yr^{-1} \ kpc^{-2}$). Using optical Keck/HIRES spectroscopy of 14 HizEA
starburst galaxies we identify outflows with maximum velocities of $820 - 2860$
\kmps. High-resolution spectroscopy allows us to measure precise column
densities and covering fractions as a function of outflow velocity and
characterize the kinematics and structure of the cool gas outflow phase (T
$\sim$10$^4$ K). We find substantial variation in the absorption profiles,
which likely reflects the complex morphology of inhomogeneously-distributed,
clumpy gas and the intricacy of the turbulent mixing layers between the cold
and hot outflow phases. There is not a straightforward correlation between the
bursts in the galaxies' star formation histories and their wind absorption line
profiles, as might naively be expected for starburst-driven winds. The lack of
strong \mgii \ absorption at the systemic velocity is likely an orientation
effect, where the observations are down the axis of a blowout. We infer high
mass outflow rates of $\rm \sim$50 $-$ 2200 $\rm M_{\odot} \, yr^{-1}$,
assuming a fiducial outflow size of 5 kpc, and mass loading factors of
$\eta\sim$5 for most of the sample. %with $\eta\sim$20 for two galaxies. While
these values have high uncertainties, they suggest that starburst galaxies are
capable of ejecting very large amounts of cool gas that will substantially
impact their future evolution.
