Dielectric spectroscopy has been employed to study the local and global dynamics of polyisoprene in the asymmetric star (polystyrene)(polyisoprene)(2) (SI2) and in the 3-miktoarm star terpolymer (polystyrene)(polyisoprene)(polybutadiene) (SIE). All measurements refer to the ordered phase where PS cylinders are embedded on the I and I/B matrix, respectively. Effectively, we are studying the local and global dynamics of tethered PI chains in two environments : one made by I-chains (SI2) and another by the I/B-chains(SIB). At low temperatures, the PI local segmental dynamics in SI2 and SIE are different, reflecting the modification of the local friction by introducing the faster PB chains in the latter. At higher temperatures, however, this effect diminishes due to the demixing of I and B. To explore the thermodynamic and mobility effects on the global dynamics, we have studied, respectively, a ternary blend composed of PI, PB, and PS and binary blends of SIB and SIE with short PB chains. The PI global dynamics in SI2 and SIE resemble the dynamics of PS stars with additional entanglement effects in the latter.