We present high sensitivity ($sigma_P simeq 0.6,$mJy) polarimetric observations in seven bands, from $2.1$ to $38,$GHz, of a complete sample of $104$ compact extragalactic radio sources brighter than $200,$mJy at $20,$GHz. Polarization measurements in six bands, in the range $5.5-38,$GHz, for $53$ of these objects were reported by citet{Galluzzi2017}. We have added new measurements in the same six bands for another 51 sources and measurements at $2.1,$GHz for the full sample of $104$ sources. Also, the previous measurements at $18$, $24$, $33$ and $38,$GHz were re-calibrated using the updated model for the flux density absolute calibrator, PKS1934-638, not available for the earlier analysis. The observations, carried out with the Australia Telescope Compact Array (ATCA), achieved a $90%$ detection rate (at $5sigma$) in polarization. $89$ of our sources have a counterpart in the $72$ to $231,$MHz GLEAM survey citep{HurleyWalker2017}, providing an unparalleled spectral coverage of $2.7$ decades of frequency for these sources. While the total intensity data from $5.5$ to $38,$GHz could be interpreted in terms of single component emission, a joint analysis of more extended total intensity spectra presented here, and of the polarization spectra, reveals that over $90%$ of our sources show clear indications of at least two emission components. We interpret this as an evidence of recurrent activity. Our high sensitivity polarimetry has allowed a $5,sigma$ detection of the weak circular polarization for $sim 38%$ of the dataset, and a deeper estimate of $20,$GHz polarization source counts than has been possible so far.
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