We present a detailed study of the effects of short branches on the rheological behaviors of H-shaped long-chain branched polymers under shear and uniaxial elongational flows using (single "phantom" chain) bead-spring Brownian dynamics simulations. To clarify the fundamental role of short branches in both flow types, the short branches are distributed either along the chain backbone or along the four dangling long arms of the H-polymer. We observe that the fast random motions of the highly mobile short branches (in association with their very short characteristic relaxation time scales) constantly disturb chain conformation, generally leading to a more compact and less deformed chain structure against the applied flow. Accordingly, the structural and dynamical properties of the short-chain branched (SCB) H-polymers in response to the flow are strongly dependent on the location of the short branches along the chain. For instance, in comparison to the original H-polymer, the H-(SCB_backbone) polymer, where the short branches are allocated along the backbone, exhibits considerably less shear-thinning behavior resulting from the lesser degree of chain alignment and structural deformation of the SCB backbone. In contrast, the H-(SCB_arm) polymer, where the short branches are allocated along the four long arms, displays a higher degree of shear-thinning behavior arising from an effective tensile force (created by the tightly coiled "superbead" character of the arms via fast short-branch dynamics) that stretches out the backbone. Importantly, the fundamental role of the short branches in determining rheological characteristics of the SCB H-polymers remains unchanged, regardless of the flow type and flow strength. (C) 2018 The Society of Rheology.