  Recent detailed simulations have shown that an insufficiently accurate
characterization of the contamination of unresolved polarized extragalactic
sources can seriously bias measurements of the primordial cosmic microwave
background (CMB) power spectrum if the tensor-to-scalar ratio $r\sim 0.001,$ as
predicted by models currently of special interest (e.g., Starobinsky's $R^2$
and Higgs inflation). This has motivated a reanalysis of the median
polarization fraction of extragalactic sources (radio-loud AGNs and dusty
galaxies) using data from the \textit{Planck} polarization maps. Our approach,
exploiting the intensity distribution analysis, mitigates or overcomes the most
delicate aspects of earlier analyses based on stacking techniques. By means of
simulations, we have shown that the residual noise bias on the median
polarization fraction, $\Pi_{\rm median}$, of extragalactic sources is
generally $\simlt 0.1\%$. For radio sources, we have found $\Pi_{\rm median}
\simeq 2.83\%$, with no significant dependence on either frequency or flux
density, in good agreement with the earlier estimate and with high-sensitivity
measurements in the frequency range 5--40\,GHz. No polarization signal is
detected in the case of dusty galaxies, implying 90\% confidence upper limits
of $\Pi_{\rm dusty}\simlt 2.2\%$ at 353\,GHz and of $\simlt 3.9\%$ at 217\,GHz.
The contamination of CMB polarization maps by unresolved point sources is
discussed.
