We analyze the phase diagrams of self-avoiding walk models of uniform branched polymers adsorbed at a surface and subject to an externally applied vertical pulling force which, at critical values, desorbs the polymer. In particular, models of adsorbed branched polymers with homeomorphism types stars, tadpoles, dumbbells and combs are examined. These models generalize earlier results on linear, ring and $3$-star polymers. In the case of star polymers we confirm a phase diagram with four phases (a free, an adsorbed, a ballistic, and a mixed phase) first seen in the paper by Janse van Rensburg EJ and Whittington SG 2018 J. Phys. A: Math. Theor. 51 204001 for $3$-star polymers. The phase diagram of tadpoles may include four phases (including a mixed phase) if the tadpole is pulled from the adsorbing surface by the end vertex of its tail. If it is instead pulled from the middle vertex of its head, then there are only three phases (the mixed phase is absent). For a dumbbell pulled from the middle vertex of a ring, there are only three phases. For combs with $t$ teeth there are four phases, independent of the value of $t$ for all $t ge 1$.
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