We study ballistic conductance in a three-terminal carbon nanotube system and show that conductance between two of the terminals can be controlled via the third terminal. The conductance is modulated by tuning the energy spectrum of the third terminal. Such a system may provide the core of a nanotransistor. We show more generally that the quasi one-dimensional nature of nanotubes can persist in branched topologies and that insights gained in analyzing one-dimensional systems can therefore be applied in analyzing networks of nanotubes.