We present the results of an observing program with the SCUBA bolometer array to measure the submillimetre (submm) dust continuum emission of 24 distant (z > 1) radio galaxies. We detected submm emission in 12 galaxies with S/N > 3, including 9 detections at z > 3. When added to previous published results these data almost triple the number of radio galaxies with z > 3 detected in the submm and yield a sample of 69 observed radio galaxies over the redshift range z = 1-5. We find that the range in rest-frame far-infrared luminosities is about a factor of 10. We have investigated the origin of this dispersion, correlating the luminosities with radio source power, size, spectral index, K-band magnitude and Lya luminosity. No strong correlations are apparent in the combined data set. We confirm and strengthen the result from previous submm observations of radio galaxies that the detection rate is a strong function of redshift. We compare the redshift dependence of the submm properties of radio galaxies with those of quasars and find that for both classes of objects the observed submm flux density increases with redshift to z ~ 4, beyond which, for the galaxies, we find tentative evidence for a decline. We find evidence for an anti-correlation between submm luminosity and UV polarisation fraction, for a subsample of 13 radio galaxies, indicating that starbursts are the dominant source of heating for dust in radio galaxies.
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