This is the third in a series of papers that present observations and results for a sample of 76 ultrasteep‐spectrum radio sources designed to find galaxies at high redshift. Here we present multifrequency radio observations, from the Australia Telescope Compact Array, for a subset of 37 galaxies from the sample. Matched resolution observations at 2.3, 4.8 and 6.2 GHz are presented for all galaxies, with the z < 2 galaxies additionally observed at 8.6 and 18 GHz. New angular size constraints are reported for 19 sources based on high‐resolution 4.8‐ and 6.2‐GHz observations. Functional forms for the rest‐frame spectral energy distributions are derived: 89 per cent of the sample is well characterized by a single power law, whilst the remaining 11 per cent show some flattening towards higher frequencies: not one source shows any evidence for high‐frequency steepening. We discuss the implications of this result in light of the empirical correlation between redshift and spectral index seen in flux‐limited samples of radio galaxies. Finally, a new physical mechanism to explain the redshift – spectral index correlation is posited: extremely steep‐spectrum radio galaxies in the local universe usually reside at the centres of rich galaxy clusters. We argue that if a higher fractions of radio galaxies, as a function of redshift, are located in environments with densities similar to nearby rich clusters, then this could be a natural interpretation for the correlation. We briefly outline our plans to pursue this line of investigation.

We present an alternative interpretation of the observations of BR 1202Ϫ0725 at and show that its z p 4.695 properties are consistent with a relativistic jet issuing from the quasar core, propagating into the intergalactic medium, and triggering star formation along its path. Prompted by this finding, we reviewed all the objects z 1 3 detected in molecular line emission and found that the distribution of gas and dust in these sources is often spatially or kinematically offset from the host galaxy and preferentially aligned along the radio axis. These observations suggest to us a scenario in which CO emission observed in high-redshift galaxies is located where it forms: along the sites of star formation triggered initially by relativistic jets.