We investigate the morphology of the [ C ii ] 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 \sim 6 - 7 , as well as a careful re-analysis of archival ALMA data . In total 29 galaxies were analysed , 21 of which are detected in [ C ii ] . For several of the latter the [ C ii ] emission breaks into multiple components . Only a fraction of these [ C ii ] components , if any , is associated with the primary UV systems , while the bulk of the [ C ii ] 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 _ { [ 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 _ { [ CII ] } -SFR relation has a weak anti-correlation with the EW ( Ly \alpha ) . The morphological analysis also reveals that [ C ii ] emission is generally much more extended than the UV emission . As a consequence , these primordial galaxies are characterised by a [ C ii ] surface brightness generally much lower than expected from the local \Sigma _ { [ CII ] } - \Sigma _ { SFR } relation . These properties are likely a consequence of a combination of different effects , namely : gas metallicity , [ C ii ] emission from obscured star-forming regions , strong variations of the ionisation parameter , and circumgalactic gas in accretion or ejected by these primeval galaxies .