Quantum dynamics on hybrid structures was introduced in a seminal paper by Exner and Seba in the 1980's. Specifically, they considered a hybrid plane made of a halfline whose origin is attached to a plane. As the evolution of many-body quantum systems can be approximated in suitable regimes by a nonlinear dynamics, it is meaningful to study the beaviour of nonlinear systems on such a hybrid plane. We illustrate the problem of the existence of the simplest solutions to the NLS, namely the Ground State, in view of a possible modeling of the Bose-Einstein condensates on hybrid traps. This is a joint project with Filippo Boni, Raffaele Carlone, and Lorenzo Tentarelli