We have developed a model to estimate the amplitude and wavelength dependence of broad-band linear polarization (BLP) from magnetic regions on cool stars. The model includes corrections both for line blends and for the partial cancellation of polarization in the vector sum over the stellar disk. Our results agree with recent calculations of BLP in the red, but show larger amplitudes and a different wavelength dependence in the blue. We find that the detailed wavelength dependence of the polarization is complex and varies with effective temperature and gravity due to changes in line blanketing. The BLP amplitudes depend strongly on field strength, blanketing, and magnetic region filling factor and geometry. We make rough estimates of the maximum BLP for stars of various spectral types and demonstrate a method for deriving a lower limit to the filling factor from the maximum observed BLP. This lower limit is related to the fractional area covered by the spatially asymmetric component of magnetic regions. Since Rayleigh and Thomson scattering are also sources of BLP. we estimate their amplitudes for a variety of cool stars. In cool dwarfs, magnetic BLP will usually dominate; only in stars of low gravity are similar levels of scattering and magnetic BLP likely. It is possible to distinguish the source of BLP by its wavelength dependence; however, to do so requires data of very high accuracy (typically a few times 10(-5)). We reanalyze some previous BLP observations to determine whether they are dominated by magnetic or Rayleigh scattering effects. In most cases, the wavelength dependence of the data admit either possibility; the polarization amplitudes, however, suggest that magnetic origins are more likely.
