A novel concept of quantum turbulence in finite size superfluids, such as trapped bosonic atoms, is discussed. We have used an atomic 87 Rb Bose-Einstein condensate (BEC) to study the emergence of this phenomenon. In our experiment, the transition to the quantum turbulent regime is characterized by a tangled vortex lines formation, controlled by the amplitude and time duration of the excitation produced by an external oscillating field. A simple model is suggested to account for the experimental observations. The transition from the nonturbulent to the turbulent regime is a rather gradual crossover. But it takes place in a sharp enough way, allowing for the definition of an effective critical line separating the regimes. Quantum turbulence emerging in a finite-size superfluid may be a new idea helpful for revealing important features associated to turbulence, a more general and broad phenomenon. Amplitude versus elapsed time diagram of magnetically excited BEC superfluid, presenting the evolution from the nonturbulent regime, with well separated vortices, to the turbulent regimes, with tangled vortices