The terminal cells of the larval Drosophila tracheal system extend dozens of branched cellular processes, most of which become hollow intracellular tubes that support gas exchange with internal tissues. Previously, we undertook a forward genetic mosaic screen to uncover the pathways regulating terminal cell size, morphogenesis, and the generation and maintenance of new intracellular tubes. Our initial work identified several mutations affecting terminal cell size and branch number, and suggested that branch complexity and cell size are typically coupled but could be genetically separated. To deepen our understanding of these processes, we have further characterized and determined the molecular identities of mutations in the genes sprout, denuded and asthmatic, that had been implicated in our initial screen. Here we reveal the molecular identity of these genes and describe their function in the context of the TOR and Hippo pathways, which are widely appreciated to be key regulators of cell and organ size.