We present a wide area (~ 8 x 8 kpc), sensitive map of CO (2-1) emission around the nearby starburst galaxy M82. Molecular gas extends far beyond the stellar disk, including emission associated with the well-known outflow as far as 3 kpc from M82s midplane. Kinematic signatures of the outflow are visible in both the CO and HI emission: both tracers show a minor axis velocity gradient and together they show double peaked profiles, consistent with a hot outflow bounded by a cone made of a mix of atomic and molecular gas. Combining our CO and HI data with observations of the dust continuum, we study the changing properties of the cold outflow as it leaves the disk. While H_2 dominates the ISM near the disk, the dominant phase of the cool medium changes as it leaves the galaxy and becomes mostly atomic after about a kpc. Several arguments suggest that regardless of phase, the mass in the cold outflow does not make it far from the disk; the mass flux through surfaces above the disk appears to decline with a projected scale length of ~ 1-2 kpc. The cool material must also end up distributed over a much wider angle than the hot outflow based on the nearly circular isophotes of dust and CO at low intensity and the declining rotation velocities as a function of height from the plane. The minor axis of M82 appears so striking at many wavelengths because the interface between the hot wind cavity and the cool gas produces Halpha, hot dust, PAH emission, and scattered UV light. We also show the level at which a face-on version of M82 would be detectable as an outflow based on unresolved spectroscopy. Finally, we consider multiple constraints on the CO-to-H$_2$ conversion factor, which must change across the galaxy but appears to be only a factor of ~ 2 lower than the Galactic value in the outflow.
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