The accretion-ejection mechanism acting in Active Galactic Nuclei (AGN) is one of the astrophysical main issues. The X-ray emission in AGN, associated with the accretion flow, is strongly coupled with the radio emission, associated with a jet. Strong X-ray versus radio correlations are found even in radio-quiet AGN, where jets are absent or very weak. To explore the origin of radio emission in radio-quiet AGN, we have surveyed the sub-parsec scale radio cores of a complete sample of well known local AGN, mapping the faintest and least luminous nuclei at a level of sub-mJy flux densities. I will present the wide variety of sub-parsec cores and structures observed, not always easy to interpret within a common physical scenario. Finally, I will discuss the possible reasons why, at milli-arcsecond resolution, the radio emission does not correlate with the X-ray emission anymore, at odds with the low efficiency accreting model predictions.