A second large programme (LP) for the physical studies of TNOs and Centaurs, started at ESO Cerro Paranal on October 2006 to obtain high-quality data, has recently been concluded. In this paper we present the spectra of these pristine bodies obtained in the visible range during the last two semesters of the LP. We investigate the spectral behaviour of the TNOs and Centaurs observed, and we analyse the spectral slopes distribution of the full data set coming from this LP and from the literature. We computed the spectral slope for each observed object, and searched for possible weak absorption features. A statistical analysis was performed on a total sample of 73 TNOs and Centaurs to look for possible correlations between dynamical classes, orbital parameters, and spectral gradient. We obtained new spectra for 28 bodies, 15 of which were observed for the first time. All the new presented spectra are featureless, including 2003 AZ84, for which a faint and broad absorption band possibly attributed to hydrated silicates on its surface has been reported. The data confirm a wide variety of spectral behaviours, with neutral--grey to very red gradients. An analysis of the spectral slopes available from this LP and in the literature for a total sample of 73 Centaurs and TNOs shows that there is a lack of very red objects in the classical population. We present the results of the statistical analysis of the spectral slope distribution versus orbital parameters. In particular, we confirm a strong anticorrelation between spectral slope and orbital inclination for the classical population. A strong correlation is also found between the spectral slope and orbital eccentricity for resonant TNOs, with objects having higher spectral slope values with increasing eccentricity.
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