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The mode-conversion behavior of branching or separating planar-dielectric waveguides is studied theoretically as a function of branch asymmetry and taper slope. When the taper slope is large in a near-symmetric structure, considerable mode conversion will occur and the structure will act as a power divider. In an asymmetric structure with small taper slope, mode conversion is negligible and the structure will act as a mode splitter. A quantitative formula is presented which can be used to determine the behavior of a given separating structure.