Abstract We present high sensitivity (σP ≃ 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 Galluzzi et al. 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, achieved a 90 per cent detection rate (at 5σ) in polarization. 89 of our sources have a counterpart in the 72–231 MHz GLEAM (GaLactic and Extragalactic All-sky Murchison Widefield Array) survey, 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 per cent 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 5σ detection of the weak circular polarization for ∼ 38 per cent of the data set, and a deeper estimate of 20 GHz polarization source counts than has been possible so far.