  We present a census of sub-pc scale properties of the VLBI cores in a
complete sample of local Seyfert galaxies. Seventeen out of 23 sources with a
VLA detection are detected also with VLBI at 1.7 GHz and/or 5 GHz, with an
average monochromatic radio luminosity log [P (5\, GHz) W Hz^{-1} = 19.4. Radio
cores are of heterogeneous nature, the majority of them showing elongated
structures or accompanied by extra components, broad ranges of brightness
temperatures (10^{5}-10^{10} K) and spectral indices (from steep to highly
inverted). Interestingly, the detection rate (26%) of water maser emission is
considerably higher than that found in previous surveys (around 10%),
suggesting that distance biases could significantly affect our knowledge of the
actual occurrence of this phenomenon. The VLBI observational properties of type
1 and type 2 nuclei are similar except for the T_{B}, which is on average
higher in type 1. These results suggest that both thermal and non-thermal
emission are common in low luminosity AGN, with a prevalence of free-free
processes among type 2 cores, likely associated to molecular gas. Though
limited by the low number statistics, we find no significant correlation
between the VLBI radio luminosity and the nuclear X-ray luminosity, the latter
appears to be more connected to the tens of pc scales VLA radio emission,
rather than to the sub-pc scales, particularly in the most X-ray luminous
sources. The X-ray radio-loudness parameter R_{X} = L (6cm)/L(2-10 keV), is on
average very low (< log R_X > = -4.8), with comparatively higher R_{X} found
for sources with the largest black hole masses and the lowest Eddington ratios,
although the radio power does not appear to depend on the accretion rate.
