  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 M82's 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.
