  A sample of large northern Spitzer Infrared Nearby Galaxies Survey (SINGS)
galaxies was recently observed with the Westerbork Synthesis Radio Telescope
(WSRT) at 1300-1760 MHz. In Paper II of this series, we described sensitive
observations of the linearly polarized radio continuum emission in this
WSRT-SINGS galaxy sample. Here we explore the systematic patterns of azimuthal
modulation of both the Faraday depth and the polarized intensity and their
variation with galaxy inclination. A self-consistent and fully general model
for both the locations of net polarized emissivity at 1-2 GHz frequencies and
the global magnetic field topology of nearby galaxies emerges. Net polarized
emissivity is concentrated into two zones located above and below the galaxy
mid-plane, with the back-side zone suffering substantial depolarization (by a
factor of 4-5) relative to the front-side zone in its propagation through the
turbulent mid-plane. The field topology, which characterizes the thick-disk
emission zone is in all cases an axisymmetric spiral with a quadrupole
dependence on height above the mid-plane. The front-side emission is affected
by only mild dispersion (10's of rad/m2) from the thermal plasma in the galaxy
halo, while the back-side emission is affected by additional strong dispersion
(100's of rad/m2) from an axisymmetric spiral field in the galaxy mid-plane.
The field topology in the upper halo of galaxies is a mix of two distinct
types: a simple extension of the axisymmetric spiral quadrupole field of the
thick disk and a radially directed dipole field. The dipole component might be
a manifestation of (1) a circumnuclear, bipolar outflow, (2) an in situ
generated dipole field, or (3) evidence of a non-stationary global halo.
