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In this article and its predecessor  , pathwise constructions of Brownian motions which satisfy all possible boundary conditions at the vertex of star graphs are given. Received 2011-11-4; Communicated by Hui-Hsiung Kuo. 2010 Mathematics Subject Classification. 60J65, 60J45, 60H99, 58J65, 35K05, 05C99.doi:10.31390/cosa.6.2.05 fatcat:5bcspnxzkjeyhet3t3hsfvqgdq