  We have studied the dependence of the AGN nuclear radio (1.4 GHz) luminosity
on both the AGN 2-10 keV X-ray and the host-galaxy K-band luminosity. A
complete sample of 1268 X-ray selected AGN (both type 1 and type 2) has been
used, which is the largest catalogue of AGN belonging to statistically well
defined samples where radio, X and K band information exists. At variance with
previous studies, radio upper limits have been statistically taken into account
using a Bayesian Maximum Likelihood fitting method. It resulted that a good fit
is obtained assuming a plane in the 3D L_R-L_X-L_K space, namely logL_R= xi_X
logL_X + xi_K logL_K + xi_0, having a ~1 dex wide (1 sigma) spread in radio
luminosity. As already shown, no evidence of bimodality in the radio luminosity
distribution was found and therefore any definition of radio loudness in AGN is
arbitrary. Using scaling relations between the BH mass and the host galaxy
K-band luminosity, we have also derived a new estimate of the BH fundamental
plane (in the L_5GHz -L_X-M_BH space). Our analysis shows that previous
measures of the BH fundamental plane are biased by ~0.8 dex in favor of the
most luminous radio sources. Therefore, many AGN studies, where the BH
fundamental plane is used to investigate how AGN regulate their radiative and
mechanical luminosity as a function of the accretion rate, or many AGN/galaxy
co-evolution models, where radio-feedback is computed using the AGN fundamental
plane, should revise their conclusions.
