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We present the largest single survey to date of average profiles of radio pulsars, observed and processed using the same telescope and data reduction software. Specifically, we present measurements for 1170 pulsars, observed by the Thousand Pulsar Array (TPA) programme at the 64-dish SARAO MeerKAT radio telescope, in a frequency band from 856 to 1712 MHz. We provide rotation measures (RM), dispersion measures, flux densities and polarization properties. The catalogue includes 254 new RMs that substantially increase the total number of known pulsar RMs. Our integration times typically span over 1000 individual rotations per source. We show that the radio (pseudo)luminosity has a strong, shallow dependence on the spin-down energy, proportional to $\dot{E}^{0.15\pm0.04}$, that contradicts some previous proposals of population synthesis studies. In addition, we find a significant correlation between the steepness of the observed flux density spectra and $\dot{E}$, and correlations of the fractional linear polarization with $\dot{E}$, the spectral index, and the pulse width, which we discuss in the context of what is known about pulsar radio emission and how pulsars evolve with time. On the whole, we do not see significant correlations with the estimated surface magnetic field strength, and the correlations with $\dot{E}$ are much stronger than those with the characteristic age. This finding lends support to the suggestion that magnetic dipole braking may not be the dominant factor for the evolution of pulsar rotation over the lifetimes of pulsars. A public data release of the high-fidelity time-averaged pulse profiles in full polarization accompanies our catalogue.