This paper presents a new grid-based method for investigating the evolution of the steep-spectrum radio luminosity function, with the aim of quantifying the high-redshift cut-off suggested by previous work. To achieve this, the Combined EIS-NVSS Survey of Radio Sources (CENSORS) has been developed; this is a 1.4 GHz radio survey, containing 135 sources complete to a flux density of 7.2 mJy, selected from the NRAO VLA Sky Survey (NVSS) over 6 deg^2 of the ESO Imaging Survey (EIS) Patch D. The sample is currently 73% spectroscopically complete, with the remaining redshifts estimated via the K-z or I-z magnitude-redshift relation. CENSORS is combined with additional radio data from the Parkes All-Sky, Parkes Selected Regions, Hercules and VLA COSMOS samples to provide comprehensive coverage of the radio power vs. redshift plane. The redshift distributions of these samples, together with radio source count determinations, and measurements of the local luminosity function, provide the input to the fitting process. The modelling reveals clear declines, at > 3sigma significance, in comoving density at z > 0.7 for lower luminosity sources (log P = 25-26); these turnovers are still present at log P > 27, but move to z > 3, suggesting a luminosity-dependent evolution of the redshift turnover, similar to the `cosmic downsizing seen for other AGN populations. These results are shown to be robust to the estimated redshift errors and to increases in the spectral index for the highest redshift sources. Analytic fits to the best-fitting steep spectrum grid are provided so that the results presented here can be easily accessed by the reader, as well as allowing plausible extrapolations outside of the regions covered by the input datasets
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