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Abstract High-velocity outflows are ubiquitous in compact, massive (M_*∼ 10¹¹M_⊙),z∼ 0.5 galaxies with extreme star formation surface densities (Σ_SFR∼ 2000M_⊙yr⁻¹kpc⁻²). We have previously detected and characterized these outflows using Mgiiabsorption lines. To probe their full extent, we present Keck/KCWI integral field spectroscopy of the [Oii] and Mgiiemission nebulae surrounding all of the 12 galaxies in this study. We find that [Oii] is more effective than Mgiiin tracing low surface brightness, extended emission in these galaxies. The [Oii] nebulae are spatially extended beyond the stars, with radial extentR₉₀between 10 and 40 kpc. The nebulae exhibit nongravitational motions, indicating galactic outflows with maximum blueshifted velocities ranging from −335 to −1920 km s⁻¹. The outflow kinematics correlate with the bursty star formation histories of these galaxies. Galaxies with the most recent bursts of star formation (within the last <3 Myr) exhibit the highest central velocity dispersions (σ≳ 400 km s⁻¹), while the oldest bursts have the lowest-velocity outflows. Many galaxies exhibit both high-velocity cores and more extended, slower-moving gas indicative of multiple outflow episodes. The slower, larger outflows occurred earlier and have decelerated as they propagate into the circumgalactic medium and mix on timescales ≳50 Myr.