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We will extend Delman's theorem and prove that a Montesinos knot $K$ of length at least 3 has a persistently laminar branched surface unless it is equivalent to $K(1/2q_1,\\, 1/q_2,\\, 1/q_3,\\, -1)$ for some positive integers $q_i$. In most cases these branched surfaces are genuine, in which case $K$ admits no atoroidal Seifert fibered surgery. 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