A Large Program (LP) has been carried out at ESO-VLT using almost simultaneously the UT1, UT2 and UT4 telescopes (Cerro Paranal, Chile). The aim of this Large Program was to obtain simultaneous visible and near-IR spectroscopic measurements (using FORS, ISAAC and SINFONI instruments) with a S/N ratio as high as possible for almost all objects among different dynamical groups observable within the VLT capability. In this paper we present results on the second half of the Large Program which includes new near-infrared spectroscopy data of 20 objects. For 12 of them for which we had obtained the complete spectral range (V + J + H + K bands), we apply a radiative transfer model to the entire spectral range to constrain their surface composition. We also present an analysis of all near-IR spectral data available on TNOs and Centaurs from both the complete LP and the literature. An overview for a total sample of 75 objects is thus carried out analyzing the ice content with respect to the physical and dynamical characteristics. The major new results are: (i) all objects classified as BB class seem to have icy surfaces; (ii) the possible presence of CH 3OH has primarily been detected on very red surfaces (RR class objects) and (iii) the majority of Centaurs observed multiple times have an heterogeneous composition.