We explore the long-term evolution of a bias-free orbital representation of the cometary nuclei (with diameters above 2 km) of the Kuiper belt, using the so-called L7 synthetic model from CFEPS, which consists of three dynamical sub-populations: the Classical, the Resonant, and the Scattering. The dynamical evolution of belt particles is studied under the gravitational influence of the Sun and the four giant planets, as well as of the 34 largest known trans-Neptunian objects (TNOs with $H_V < 4$). Here we indistinctly call Dwarf Planets (DPs) to the full sample of 34 large TNOs. Over a 1 Gyr timescale, we analyze the secular influence of the DPs over Kuiper belt disk particles and their contribution to the injection rate of new visible Jupiter Family Comets (JFCs). We found that DPs globally increase the number of JFCs by 12.6% when compared with the comets produced by the giant planets alone. When considering each population separately, we find that the increment produced by DPs is 17%, 12%, and 3% for the Classical, Resonant, and Scattering populations, respectively. Given the rate of escapes from the Kuiper belt, we find upper limits to the number of objects in each population required to maintain the JFCs in steady-state; the results are $55.9times10^6$, $78.5times10^6$, and $274.3times10^6$ for the Scattering, Resonant, and Classical populations, respectively. Finally, we find that the Plutinos are the most important source of comets which were originally in a resonant configuration, where the presence of Pluto alone enhances by 10% the number of JFCs.
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