Almost 20 years of observations of the trans-Neptunian region have shed light on the overall dynamical structure of the trans-Neptunian object (TNO) populations and absolute magnitude distributions. The TNO region can be inserted in the global frame of the dynamical evolution of the giant planets, as described by the Nice model. Any reliable collisional evolution model should account for dynamical effects and should produce results that meet the constraints imposed by current observables. With this aim, we have developed a code package [Asteroid-LIke Collisional ANd Dynamical Evolution Package (alicandep)], which is a collisional evolution code that includes statistical elimination of objects by dynamical effects within the frame of a disc migrating and gradually dynamically exciting, as well as the dynamical migration of objects between regions. Moreover, we included the possibility to distinguish between dynamically cold and hot bodies in the main classical belt and to keep track of primordial bodies in the whole region. Finally, we performed a large number of numerical simulations varying physical parameters, boundary and initial conditions, in order to match the current observables and the dynamical conditions of the Nice model. Our results are in agreement with those observables and can explain the flattened size distributions in the 30–100 km size range. This allows us to constrain the original mass of the belt (not less than 50 M⊕), which is compatible with initial shallow size distributions below 100 km. alicandep also finds an extremely high probability for the existence of at least one more large (>1700 km) object yet to be discovered in the outer belt. This model supports the reliability of the Nice model, and it can be a suitable tool to statistically study many features of the trans-Neptunian region.