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Surface plasmon (SP) vortices typically have annular intensity patterns. Here we show that fractional SP vortices with arbitrary, asymmetric intensity patterns can be synthesized via simple geometric arrangements. We provide the direct experimental observations over the existence of fractional SP vortices. Triangular SP vortex intensities are synthesized by circularly polarized plane waves. On the other hand, subwavelength focusing with user-desired patterns is also experimentally demonstrated. The synthesized SP vortex and focusing patterns are experimentally measured using a near-field scanning optical microscope with uncoated fiber probe and are found in good agreements as compared to numerical results.