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In the previous two papers, namely, \citet{anuknn11} and \citet{anuetal11} wesolved the polarized radiative transfer (RT) equation in multi-dimensional(multi-D) geometries, with partial frequency redistribution (PRD) as thescattering mechanism. We assumed Rayleigh scattering as the only source oflinear polarization ($Q/I, U/I$) in both these papers. In this paper we extendthese previous works to include the effect of weak oriented magnetic fields(Hanle effect) on line scattering. We generalize the technique of Stokes vectordecomposition in terms of the irreducible spherical tensors $\mathcal{T}^K_Q$,developed in \citet{anuknn11}, to the case of RT with Hanle effect. A fastiterative method of solution (based on the Stabilized PreconditionedBi-Conjugate-Gradient technique), developed in \citet{anuetal11}, is nowgeneralized to the case of RT in magnetized three-dimensional media. We use theefficient short-characteristics formal solution method for multi-D media,generalized appropriately to the present context. The main results of thispaper are the following: (1) A comparison of emergent $(I, Q/I, U/I)$ profilesformed in one-dimensional (1D) media, with the corresponding emergent,spatially averaged profiles formed in multi-D media, shows that in thespatially resolved structures, the assumption of 1D may lead to large errors inlinear polarization, especially in the line wings. (2) The multi-D RT insemi-infinite non-magnetic media causes a strong spatial variation of theemergent $(Q/I, U/I)$ profiles, which is more pronounced in the line wings. (3)The presence of a weak magnetic field modifies the spatial variation of theemergent $(Q/I, U/I)$ profiles in the line core, by producing significantchanges in their magnitudes.

Polarized Line Formation in Multi-Dimensional Media.III. Hanle Effect with Partial Frequency Redistribution