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The linear polarization of broad emission lines from anisotropically expanding clouds in active galactic nuclei (AGN) is calculated using a Monte Carlo method. Both semi-forbidden and permitted lines are considered. We investigate the effect of spatial transport and geometric anisotropy on polarization. In general, higher polarization is obtained from the transitions with small angular momenta. The maximum polarization of 8 percent is obtained from a single stationary oblate cloud and 4 percent from a stationary prolate cloud when the optical depth $\tau$ is $\sim 1$ with large axis ratios, and this condition may be satisfied by some semi-forbidden lines which have the optical depth $\tau\sim 1-10$ (\eg CIII]$\lambda 1909$). Similar results are obtained from expanding clouds depending on the optical depths and kinematic conditions. The numerical integration over a disk-like configuration of emission clouds shows 4 percent or lower polarization compared to a single cloud. An illustrative application to a model of broad absorption line quasars is discussed.
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