  Ultra-deep radio surveys are an invaluable probe of dust-obscured star
formation, but require a clear understanding of the relative contribution from
radio AGN to be used to their fullest potential. We study the composition of
the $\mu$Jy radio population detected in the Karl G. Jansky Very Large Array
COSMOS-XS survey based on a sample of 1540 sources detected at 3 GHz over an
area of $\sim350\text{arcmin}^2$. This ultra-deep survey consists of a single
pointing in the well-studied COSMOS field at both 3 and 10 GHz and reaches
RMS-sensitivities of $0.53$ and $0.41\mu$Jy beam$^{-1}$, respectively. We find
multi-wavelength counterparts for $97\%$ of radio sources, based on a
combination of near-UV/optical to sub-mm data, and through a stacking analysis
at optical/near-infrared wavelengths we further show that the sources lacking
such counterparts are likely to be high-redshift in nature (typical
$z\sim4-5$). Utilizing the multi-wavelength data over COSMOS, we identify AGN
through a variety of diagnostics and find these to make up $23.2\pm1.3\%$ of
our sample, with the remainder constituting uncontaminated star-forming
galaxies. However, more than half of the AGN exhibit radio emission consistent
with originating from star-formation, with only $8.8\pm0.8\%$ of radio sources
showing a clear excess in radio luminosity. At flux densities of $\sim30\mu$Jy
at 3 GHz, the fraction of star-formation powered sources reaches $\sim90\%$,
and this fraction is consistent with unity at even lower flux densities.
Overall, our findings imply that ultra-deep radio surveys such as COSMOS-XS
constitute a highly effective means of obtaining clean samples of
star-formation powered radio sources.
