We present a study of the dynamical evolution of plutinos recently escaped from the resonance through numerical simulations. It was shown in previous works the existence of weakly chaotic orbits in the plutino population that diffuse very slowly finally diving into a strong chaotic region. These orbits correspond to long-term plutino escapers and then represent the plutinos that are escaping from the resonance at present. Then, we divided the numerical simulation in two parts. First, we develop a numerical simulation of 20,000 test particles in the resonance in order to detect the long-term escapers. We set the initial orbital elements such that cover the present observational range of orbital elements of plutinos. Second, we perform a numerical simulation of the selected escaped plutinos in order to study their dynamical post escaped behavior. We describe and characterize the routes of escape of plutinos and their evolution in the Centaur zone. Also, we obtain that Centaurs coming from plutinos would represent a fraction of less than 6% of the total Centaur population.