In this paper, the simulator COCA, a novel fully three-dimensional (3-D) finite-element (FE) tool for the design of multistage depressed TWTs collectors is illustrated. COCA has been developed at the University of Catania under an ESA/ESTEC project. The complete simulator consists of three main modules: a fully 3-D deterministic/neural FE mesh generator, an FE Vlasov solver coupled with an electron trajectory tracer taking into account also external magnetic fields, and a postprocessing module for result restitution, including secondary electron emission effects. All the functions are interactively managed and executed by means of an especially developed user-friendly graphical user interface which controls all the various aspects of a simulation session. The results of a simulation test performed on an asymmetric collector are also reported showing excellent agreement with available measured data. The COCA simulator provides the user with flexible and effective tools to design, test, optimize, and verify innovative asymmetrical geometries for TWT collectors.