  We present near-infrared spectra, obtained with SINFONI and XShooter
observations at ESO VLT, of nine dusty, red QSOs at 1.2<z<2.6. The sources are
hard X-ray detected, characterized by cold absorption (N_H>10^{21} - 10^{22}
cm^{-2}) and show a broad Ha component in the NIR spectra. We complement this
sample with twelve additional sources taken from the literature with similar
properties resulting in a total sample of 21 X-ray obscured, intermediate type
(1.8-1.9), dusty reddened QSOs. From the broad Ha line we have computed the BH
masses through the virial formula and derived Eddington ratios. Moreover, from
optical/IR multi-component SED fitting we have derived the stellar mass of
their host galaxies and their SFRs. We find that most of the sources in our
sample are hosted in starburst and main sequence star-forming galaxies with
Eddington ratios lambda>0.1. We find a strong trend with the BH mass i.e. less
massive objects are scattered below and above the local relation while the most
massive ones are mainly located above it. We also studied the evolution of
these sources on the M_BH-M_star plane compared to a sample of optically blue
type--1 QSOs and we find that obscured red QSOs show a ratio of M_BH to M_star
that increases with redshift which is consistent with or slightly lower than
what has been found for blue QSOs. These sources may represent the blow-out
phase at the end of the rapid BH growth and immediately preceding the classical
blue QSOs typically sampled in optical surveys. They in fact show evidence of
outflows in the ionized gas component, but their BH has already fully formed.
