The LOFAR Two-metre Sky Survey: VII. Third Data Release
We present the third data release of the LOFAR Two-metre Sky Survey (LoTSS-DR3). The survey images cover 88% of the northern sky and were created from 12,950 hrs of data (18.6 PB) accumulated over 10.5 years. The images were produced through direction-independent and direction-dependent calibration pipelines that correct for instrumental effects as well as spatially and temporally varying ionospheric distortions. In our 120-168 MHz continuum mosaic images with an angular resolution of 6 arcsec (9 arcsec below declination 10$^\circ$) we catalogue 13,667,877 sources, formed from 16,943,656 Gaussian components. The scatter in the astrometric precision approximately follows the expected noise-like behaviour but with an additional systematic component of at least 0.24 arcsec that is likely due to calibration imperfections. The random flux density scale error is 6%, while the systematic offset was previously shown to be within 2%. The median sensitivity of our mosaics is 92$\mu$Jy beam$^{-1}$. Completeness simulations, accounting for realistic source models, time- and bandwidth-smearing effects, and astrometric errors, indicate that we detect more than 95% of compact sources with integrated flux densities exceeding 9 times the local root mean square (RMS) noise. However, the recovered source counts in a particular integrated flux density bin do not match the injected counts until flux densities exceed 45 times the local RMS noise. The Euclidean-normalised differential source counts derived from the survey constrain the radio source population over five orders of magnitude and are in good agreement with previous deep and wide-area surveys. All data products are publicly available, including catalogues, individual-field Stokes I, Q, U, and V images, mosaicked Stokes I images, and $uv$ data with associated direction-dependent calibration solutions.