We use molecular dynamics computer simulations to investigate complexation and clustering of branched polymers. In this study, we focus on star and bottle-brush polymers. In our investigation, we identify key factors governing cluster formation of branched amphiphilic polymers and provide guidance for designing and preparing various types of polymer clusters for applications, e.g., in drug delivery or materials science. We observe different kinds of clustering in the polymer systems. Our star polymers consist of several arms of hydrophilic core particles with hydrophobic particles attached to the end of each star arm. We observe that amphiphilic star polymers generally tend to form spherical complexes. In contrast to this, bottle-brush polymers exhibit a larger variety of complex structures. With large grafting density and large side arms, we also observe spherical polymer clusters; however, for low grafting density and shorter side chains, distinct clusters connected by bridging particles are formed. Furthermore, we observe membrane-like clustering of bottle-brush polymers. We employ two different clustering algorithms for further analysis of the obtained structures with respect to shape factors, pair correlation functions, and radii of gyration. We find that the hydrophobic parts of polymers play a crucial role in the formation of the resulting structures during self-assembly. The hydrophilic core parts in star polymers along with steric hindrance lead to a screening effect for the hydrophobic parts of the polymers. With bottle-brush copolymers, the hydrophilic parts of the polymers exhibit a screening effect that is sensitive to the grafting density and side chain lengths along the backbone.