We present a numerical study of three-layer graphene heterostructures in which the layers are twisted by the magic angle ($\sim 1.1^{\circ }$) or by $\sim {30}^{\circ }$ to form a graphene quasicrystal. The heterostacks are described using realistic structural relaxations and tight-binding Hamiltonians, and their transport properties are computed for both pristine and disordered systems containing up to $\sim 8$ million atoms. Owing to the weak interlayer coupling, we resolve the hybridization between magic-angle flat bands and quasicrystalline states, which are modified in distinct ways across low- and high-energy windows, revealing a different hybrid electronic regime to explore.

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• Electrical conductivity
• Proximity effect
• Quantum transport
• Quasicrystals
• Twisted bilayer graphene
• Twisted heterostructures
• Tight-binding model