Carbon nanotube thin-film transistors are expected to enable the fabrication of high-performance, flexible and transparent devices using relatively simple techniques. However, as-grown nanotube networks usually contain both metallic and semiconducting nanotubes, which leads to a trade-off between charge-carrier mobility (which increases with greater metallic tube content) and on/off ratio (which decreases). Many approaches to separating metallic nanotubes from semiconducting nanotubes have been investigated, but most lead to contamination and shortening of the nanotubes, thus reducing performance. Here, we report the fabrication of high-performance thin-film transistors and integrated circuits on flexible and transparent substrates using floating-catalyst chemical vapour deposition followed by a simple gas-phase filtration and transfer process. The resulting nanotube network has a well-controlled density and a unique morphology, consisting of long (~10 µm) nanotubes connected by low-resistance Y-shaped junctions. The transistors simultaneously demonstrate a mobility of 35 cm(2) V(-1) s(-1) and an on/off ratio of 6 × 10(6). We also demonstrate flexible integrated circuits, including a 21-stage ring oscillator and master-slave delay flip-flops that are capable of sequential logic. Our fabrication procedure should prove to be scalable, for example, by using high-throughput printing techniques.