Mean recovered cross-power spectra from realistic simulations of Planck CMB lensing convergence and NVSS or TGSS data maps (in green). The spectra are consistent with zero, demonstrating that our analysis pipeline does not induce spurious cross-power in the absence of correlation (see text). Error bars are the diagonal elements of the empirical covariance matrix derived from the same simulations. They need to be compared with the gray bands that represent the analytic Gaussian uncertainties used throughout the paper. In the top panel, in orange, we also show the mean cross-power spectrum from Gaussian-correlated lensing and galaxy simulations minus the input theoretical cross-power spectrum. Consistency with zero implies that our pipeline is able to recover in an unbiased way a known input cross-spectrum. Error bars in this case are the diagonal elements of the empirical covariance matrix derived from the correlated simulations.