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tokens: These results have important implicationsfor the delivery of water to the asteroid belt and on Earth, as also suggested by previous studies focusing on the in situ formation or a more limited migration of the giant planets ( Turrini et al. 2011 ; Turrini Svetsov 2014 ; Grazier et al. 2014 ). Raymond Izidoro (2017a ) simulated both an in situ growth and a large scale migration ofthe giant planets including gas drag. They found that a fraction of objects from beyond the current position of Jupiter are implanted in the main asteroid belt during the growth of the giant planets, generating a large-scale mixing of the small bodies. The source region of implanted asteroids was from 4 to 9 au in the in situ scenario, identified as the precursors of the C -type asteroids, and from 4 to 15 when migration was taken into account. In our migration model, we also found implanted bodies from 4 to 16 au in the asteroid belt, but most of them, 96.6%, come from 4 to 5 au region (that end up piled up in the 2:1 resonance with Jupiter at about 3 au as shown in Figs. 4 and 5 ) and just 3.4% of them come from 6 to 16 au. Differently from Raymond Izidoro (2017a ), we did not simulate the preexisting asteroid belt for computational time reasons, but we can analyse our results considering a preexisting “virtual” asteroid belt composed by S- and C- type asteroids, with the S-type dominating the inner belt and C-types more common in the outer belt. Taking into account the Minimum Mass Solar Nebula, the asteroid belt mass is about 1 M ⊕ . From the same assumption, a particle in our simulations carries 5 × 10 −5 M ⊕ and thus we can make a crude estimation of the mass that is injected in the asteroid belt. From the 5 Myr snapshots we counted the particles that ended up in the asteroid belt. The results are that in the nominal model, roughly 1 M ⊕ of outer solar system planetesimals are injected into the asteroid belt. This number is to be compared to the amount of mass in the primordial asteroid belt, that is roughly 1 M ⊕ . Hence, after the migration, about 50% of the belt is composed of outer solar system planetesimals. The nominal model is the most efficient in injecting bodies into the asteroid belt and the least efficient ones are the in situ model and the growth tracks 2.0 times faster than the nominal model, both inject only ~0.2 M ⊕ . It is important to notice that, in this model, 96.6% of the mass injected in the belt resides in the 2:1 resonance and a subsequent instability of the giant planets after the disc dispersal can affect dramatically this resonant region, depleting it almost completely. We will show this result in Sect. 5 . This will reduce drastically the contamination of the belt, leaving just 10 −2 M ⊕ of P and D type asteroids in the belt to be compared with the 1 M ⊕ preexisting belt. Even though the contamination is not so important in terms of mass, secular erosion of the mass of the asteroid belt only accounts for 50% of the its mass loss (