  Past observations of QSO host galaxies at z >6 have found cold gas and star
formation on compact scales of a few kiloparsecs. We present new high
sensitivity IRAM PdBI follow-up observations of the [CII] 158micron emission
line and FIR continuum in the host galaxy of SDSS J1148+5152, a luminous QSO at
redshift 6.4189. We find that a large fraction of the gas traced by [CII] is at
high velocities, up to ~1400 km/s relative to the systemic velocity, confirming
the presence of a major quasar-driven outflow indicated by previous
observations. The outflow has a complex morphology and reaches a maximum
projected radius of ~30 kpc. The extreme spatial extent of the outflow allows
us, for the first time in an external galaxy, to estimate mass-loss rate,
kinetic power and momentum rate of the outflow as a function of the projected
distance from the nucleus and the dynamical time-scale. These trends reveal
multiple outflow events during the past 100 Myr, although the bulk of the mass,
energy and momentum appear to have been released more recently, within the past
~20 Myr. Surprisingly, we discover that also the quiescent gas at systemic
velocity is extremely extended. More specifically, we find that, while 30% of
the [CII] within v\in(-200, 200) km/s traces a compact component that is not
resolved by our observations, 70% of the [CII] emission in this velocity range
is extended, with a projected FWHM size of 17.4+-1.4 kpc. We detect FIR
continuum emission associated with both the compact and the extended [CII]
components, although the extended FIR emission has a FWHM of 11+-3 kpc, thus
smaller than the extended [CII] source. Overall, our results indicate that the
cold gas traced by [CII] is distributed up to r~30 kpc. A large fraction of
extended [CII] is likely associated with star formation on large scales, but
the [CII] source extends well beyond the FIR continuum.
