In this work we report the effect of the hard block dianhydride structure on the overall properties of partially biobased semiaromatic polyimides. For the study, four polyimides were synthesized using aliphatic fatty dimer diamine (DD1) as the soft block and four different commercially available aromatic dianhydrides as the hard block: 4,4'-(4,4'-isopropylidenediphenoxy) bis(phthalic anhydride) (BPADA), 4,4'-oxidiphthalic anhydride (ODPA), 4,4'-(Hexafluoroisopropylidene) diphthalic anhydride (6FDA), and 3,3',4,4'-biphenyltetracarboxylic dianhydride (BPDA). The polymers synthesized were fully organo-soluble thermoplastic branched polyimides with glass transition temperatures close to room temperature. The detailed analysis took into account several aspects of the dianhydrides structure (planarity, rigidity, bridging group between the phtalimides, and electronic properties) and related them to the results obtained by differential scanning calorimetry, rheology, fluorescence and broadband dielectric spectroscopy. Moreover, the effects of physical parameters (crystallization and electronic interactions) on the relaxation behavior are discussed. Despite the presence of the bulky branched soft block given by the dimer diamine, all polyimides showed intermolecular charge transfer complexes, whose extent depends on the electronic properties of the dianhydride hard block. Furthermore, the results showed that polyimides containing flexible and bulky hard blocks turned out fully amorphous while the more rigid dianhydride (BPDA) led to a nanophase separated morphology with low degree of crystallinity resulting in constrained segmental relaxation with high effect on its mechanical response with the annealing time. This work represents the first detailed report on the development and characterization of polyimides based on a biobased fatty dimer diamine. The results highlight the potential of polymer property design by controlled engineering of the aromatic dianhydride blocks.