Since the discovery of superconductivity and correlated insulators at fractional electron fillings in twisted bilayer graphene, most theoretical efforts have been focused on describing this system in terms of an effective extended Hubbard model. However, it was recognized that an exact tight-binding model on the moiré superlattice which captures all the subtleties of the bands can be exceedingly complicated. Here, we pursue an alternative framework of coupled wires to describe the system based on the observation that the lattice relaxation effect is strong at small twist angles, which substantially enlarges the AB and BA stacking domains. Under an out-of-plane electric field which can have multiple origins, the low-energy physics of the system is dominated by interconnected wires with (approximately) gapless one-dimensional (1D) conducting quantum valley Hall domain wall states. We demonstrate that the Coulomb interaction likely renders the wires a U(2)2 (1+1)D conformal field theory (CFT) with a tunable Luttinger parameter for the charge U(1) sector. Spin-triplet and spin-singlet Cooper pair operators both have quasi-long-range order in this CFT. The junction between the wires at the AA stacking islands can lead to either a two-dimensional superconductor, or an insulator. © 2019 American Physical Society.