  Recent deep and wide radio surveys extend the studies for radio-excess active
galactic nuclei (radio-AGNs) to lower luminosities and higher redshifts,
providing new insights into the abundance and physical origin of radio-AGNs.
Here we focus on the cosmic evolution, physical properties and AGN-host galaxy
connections of radio-AGNs selected from a sample of ~ 500,000 galaxies at 0 < z
< 4 in GOODS-N, GOODS-S, and COSMOS fields. Combining deep radio data with
multi-band, de-blended far-infrared (FIR) and sub-millimeter data, we identify
1162 radio-AGNs through radio excess relative to the FIR-radio relation. We
study the cosmic evolution of 1.4 GHz radio luminosity functions (RLFs) for
star-forming galaxies (SFGs) and radio-AGNs, which are well described by a pure
luminosity evolution of $L_*\propto (1+z)^{-0.31z+3.41}$ and a pure density
evolution of $\Phi_*\propto (1+z)^{-0.80z+2.88}$, respectively. We derive the
turnover luminosity above which the number density of radio-AGNs surpasses that
of SFGs. This crossover luminosity increases as increasing redshift, from
$10^{22.9}$ W Hz$^{-1}$ at z ~ 0 to $10^{25.2}$ W Hz$^{-1}$ at z ~ 4. At full
redshift range (0 < z < 4), we further derive the probability ($p_{radio}$) of
SFGs and quiescent galaxies (QGs) hosting a radio-AGN as a function of stellar
mass ($M_*$), radio luminosity ($L_R$), and redshift (z), which yields
$p_{radio}\propto (1+z)^{3.54}M_*^{1.02}L_R^{-0.90}$ for SFGs, and
$p_{radio}\propto (1+z)^{2.38}M_*^{1.39}L_R^{-0.60}$ for QGs, respectively. It
indicates that radio-AGNs in QGs prefer to reside in more massive galaxies with
larger $L_R$ than those in SFGs, and radio-AGN fraction increases towards
higher redshift in both SFGs and QGs with a more rapid increase in SFGs.
Further, we find that the radio-AGN fraction depends on accretion states of BHs
and redshift in SFGs, while in QGs it also depends on BH (or galaxy) mass.
