The Australia Telescope 20 GHz ( AT20G ) survey is a blind survey of the whole Southern sky at 20 GHz with follow-up observations at 4.8 , 8.6 , and 20 GHz carried out with the Australia Telescope Compact Array ( ATCA ) from 2004 to 2008 .
In this paper we present an analysis of radio spectral properties in total intensity and polarisation , sizes , optical identifications , and redshifts of the sample of the 5808 extragalactic sources in the survey catalogue of confirmed sources over 6.1 sr in the Southern sky ( i.e .
the whole Southern sky excluding the strip at Galactic latitude |b| < 1.5 ^ { \circ } ) .

The sample has a flux density limit of 40 mJy .
Completeness has been measured as a function of scan region and flux density .
Averaging over the whole survey area the follow-up survey is 78 % complete above 50 mJy and 93 % complete above 100 mJy .
3332 sources with declination \delta < -15 ^ { \circ } have good quality almost simultaneous observations at 4.8 , 8.6 , and 20 GHz .
The spectral analysis shows that the sample is dominated by flat-spectrum sources , with 69 % having spectral index \alpha _ { 8.6 } ^ { 20 } > -0.5 ( S \propto \nu ^ { \alpha } ) .
The fraction of flat-spectrum sources decreases from 81 % for S _ { 20 GHz } > 500 Â mJy , to 60 % for S _ { 20 GHz } < 100 Â mJy .
There is also a clear spectral steepening at higher frequencies with the median \alpha decreasing from -0.16 between 4.8 and 8.6Â GHz to -0.28 between 8.6 and 20Â GHz .

Simultaneous observations in polarisation are available for all the sources at all the frequencies .
768 sources have a good quality detection of polarised flux density at 20 GHz ; 467 of them were also detected in polarisation at 4.8 and/or at 8.6 GHz so that it has been possible to compare the spectral behaviour in total intensity and polarisation .
We have found that the polarised fraction increases slightly with frequency and decreases with flux density .
The spectral indices in total intensity and in polarisation are , on average , close to each other , but we also found several sources for which the spectral shape of the polarised emission is substantially different from the spectral shape in total intensity .
The correlation between the spectral indices in total intensity and in polarisation is weaker for flat-spectrum sources .

Cross matches and comparisons have been made with other catalogues at lower radio frequencies , and in the optical , X-ray and \gamma -ray bands .
Redshift estimates are available for 825 sources .