  Aims: We evaluate the radial velocity (RV) information content and achievable
precision on M0-M9 spectra covering the ZYJHK bands. We do so while considering
both a perfect atmospheric transmission correction and discarding areas
polluted by deep telluric features, as done in previous works.
  Methods: To simulate the M-dwarf spectra, PHOENIX-ACES model spectra were
employed; they were convolved with rotational kernels and instrumental profiles
to reproduce stars with a $v.sin{i}$ of 1.0, 5.0, and 10.0 km/s when observed
at resolutions of 60 000, 80 000, and 100 000. We considered the RV precision
as calculated on the whole spectra, after discarding strongly polluted areas,
and after applying a perfect telluric correction. In our simulations we paid
particular attention to the details of the convolution and sampling of the
spectra, and we discuss their impact on the final spectra.
  Results: Our simulations show that the most important parameter ruling the
difference in attainable precision between the considered bands is the spectral
type. For M0-M3 stars, the bands that deliver the most precise RV measurements
are the Z, Y, and H band, with relative merits depending on the parameters of
the simulation. For M6-M9 stars, the bands show a difference in precision that
is within a factor of $\sim$2 and does not clearly depend on the band; this
difference is reduced to a factor smaller than $\sim$1.5 if we consider a
non-rotating star seen at high resolution. We also show that an M6-M9 spectrum
will deliver a precision about two times better as an M0-M3 spectra with the
same signal-to-noise ratio. Finally, we note that the details of modelling the
Earth atmosphere and interpreting the results have a significant impact on
which wavelength regions are discarded when setting a limit threshold at 2-3%.
(abridged)
