  We investigate the morphology of the [CII] emission in a sample of "normal"
star-forming galaxies at $5<z<7.2$ in relation to their UV (rest-frame)
counterpart. We use new ALMA observations of galaxies at $z\sim6-7$ as well as
a careful re-analysis of archival ALMA data. In total 29 galaxies were
analysed, 21 of which are detected in [CII]. For several of the latter the
[CII] emission breaks into multiple components. Only a fraction of these [CII]
components, if any, is associated with the primary UV systems, while the bulk
of the [CII] emission is associated either with fainter UV components, or not
associated with any UV counterpart at the current limits. By taking into
account the presence of all these components, we find that the L$_{\rm
[CII]}$-SFR relation at early epochs is fully consistent with the local
relation, but it has a dispersion of 0.48$\pm$0.07 dex, which is about two
times larger than observed locally. We also find that the deviation from the
local L$_{\rm [CII]}$-SFR relation has a weak anti-correlation with the
EW(Ly$\alpha$). The morphological analysis also reveals that [CII] emission is
generally much more extended than the UV emission. As a consequence, these
primordial galaxies are characterised by a [CII] surface brightness generally
much lower than expected from the local ${\rm \Sigma_{[CII}-\Sigma_{SFR}}$
relation. These properties are likely a consequence of a combination of
different effects, namely: gas metallicity, [CII] emission from obscured
star-forming regions, strong variations of the ionisation parameter, and
circumgalactic gas in accretion or ejected by these primeval galaxies.
