We have identified 7824 radio sources from the 1.4 GHz NRAO VLA Sky Survey ( NVSS ) with galaxies brighter than K = 12.75 mag .
in the Second Incremental Data Release of the 6dF Galaxy Survey ( 6dFGS DR2 ) .
The resulting sample of redshifts and optical spectra for radio sources over an effective sky area of 7076 deg ^ { 2 } ( about 17 per cent of the celestial sphere ) is the largest of its kind ever obtained .
NVSS radio sources associated with galaxies in the 6dFGS span a redshift range 0.003 < z < 0.3 and have median \tilde { z } = 0.043 .
Through visual examination of 6dF spectra we have identified the dominant mechanism for radio emission from each galaxy .
60 per cent are fuelled by star-formation and 40 per cent are fuelled by an active galactic nucleus powered by a supermassive black hole .
We have accurately determined the local radio luminosity function at 1.4 GHz for both classes of radio source and have found it to agree well with other recent determinations .
From the radio luminosity function of star-forming galaxies we derive a local star formation density of 0.022 \pm 0.001 M _ { \odot } yr ^ { -1 } Mpc ^ { -3 } , in broad agreement with recent determinations at radio and other wavelengths .

We have split the radio luminosity function of radio-loud AGN into bins of absolute K -band magnitude ( M _ { K } ) and compared this with the underlying K -band galaxy luminosity function of all 6dFGS galaxies to determine the bivariate radio- K -band luminosity function .
We verify that radio-loud AGN preferentially inhabit the brightest and hence most massive host galaxies and show that the fraction of all galaxies which host a radio-loud AGN scales as f _ { radio - loud } \propto L _ { K } ^ { 2.1 } for f _ { radio - loud } < 0.3 , indicative of a similarly strong scaling with black hole mass and stellar mass .