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Arborescent (dendrigraft) polymers are known to be the class of dendritic molecules of high molecular weight. In contrast to hyperbranched molecules and similarly to dendrimers, the arborescent polymers can be obtained with a well-defined molecular structure - their inital “building blocks” are monodisperse linear chains, which are succusessively “grafted onto” the polymeric substrate by generation-based scheme. The number of grafts and their chemical compostition in each generation can be varied and thus the highly branched copolymers can be achieved. Such multi-component molecules can be used in number of contemporary applications such as templates for nanoparticles with defined shape and form, efficient microemulsion stabilizers or even building blocks of complex molecular aggregates in polymer melts and solutions. In the present research we have performed a series of computer experiments using the dissipative particle dynamics simulation technique (DPD) to study the arborescent copolymers of particular architecture shown in Figure 1 in following cases: (a) single molecules in a selective solvent; (b) molecular self-assembly in solution; (c) the mixture of arborescent molecules and linear diblock-copolymers with identical chemical composition. In particular, the results of our simulations revealed the existence of network-like aggregates formed by the considered molecules in solutions under certain conditions and stability of gyroid-like structures in the melt. We believe that our findings could be useful in obtaining of stimuli-responsive solutions and block copolymer films with stable 3D percolated morphologies.