We present a Monte Carlo time-domain study of nanostructured ballistic three-branch junctions (TBJs) excited by both step-function and Gaussian picosecond transients. Our TBJs were based on InGaAs 2-dimensional electron gas heterostructures and their geometry followed exactly the earlier experimental studies. Time-resolved, picosecond transients of both the central branch potential and the between-the-arms current demonstrate that the bandwidth of the intrinsic TBJ response reaches the THz frequency range, being mainly limited by the large-signal, intervalley scattering, when the carrier transport regime changes from ballistic to diffusive.