  We present here the final results of the first spectropolarimetric survey of
a small sample of active M dwarfs, aimed at providing observational constraints
on dynamo action on both sides of the full-convection threshold (spectral type
M4). Our two previous studies (Donati et al. 2008b; Morin et al. 2008b) were
focused on early and mid M dwarfs. The present paper examines 11 fully
convective late M dwarfs (spectral types M5-M8). Tomographic imaging techniques
were applied to time-series of circularly polarised profiles of 6 stars, in
order to infer their large-scale magnetic topologies. For 3 other stars we
could not produce such magnetic maps, because of low variability of the Stokes
V signatures, but were able to derive some properties of the magnetic fields.
We find 2 distinct categories of magnetic topologies: on the one hand strong
axisymmetric dipolar fields (similar to mid M dwarfs), and on the other hand
weak fields generally featuring a significant non-axisymmetric component, and
sometimes a significant toroidal one. Comparison with unsigned magnetic fluxes
demonstrates that the second category of magnetic fields shows less
organization (less energy in the large scales), similarly to partly convective
early M dwarfs. Stars in both categories have similar stellar parameters, our
data do not evidence a separation between these 2 categories in the
mass-rotation plane. We also report marginal detection of a large-scale
magnetic field on the M8 star VB 10 featuring a significant toroidal
axisymmetric component, whereas no field is detectable on VB 8 (M7).
