  The transfer of polarized radiation in stochastic synchrotron sources is
explored by means of analytic treatment and Monte Carlo simulations. We argue
that the main mechanism responsible for the circular polarization properties of
compact synchrotron sources is likely to be Faraday conversion and that,
contrary to common expectation, a significant rate of Faraday rotation does not
necessarily imply strong depolarization. The long-term persistence of the sign
of circular polarization, observed in many sources, is most likely due to a
small net magnetic flux generated in the central engine, carried along the jet
axis and superimposed on a highly turbulent magnetic field. We show that the
mean levels of circular and linear polarizations depend on the number of field
reversals along the line of sight and that the gradient in Faraday rotation
across turbulent regions can lead to ``correlation depolarization''. Our model
is potentially applicable to a wide range of synchrotron sources. In
particular, we demonstrate how our model can naturally explain the excess of
circular over linear polarization in the Galactic Center and the nearby spiral
galaxy M81 and discuss its application to the quasar 3C 279, the intraday
variable blazar PKS 1519-273 and the X-ray binary SS 433.
