  (ABRIDGED)
  Aims: We discuss and characterize micro-lensing among the 3 brightest lensed
images (A-B-C) of the gravitational lens system RXS J1131-1231 (a quadruply
imaged AGN) by means of long slit optical and NIR spectroscopy. Qualitative
constraints on the size of different emission regions are derived.
  Methods: We decompose the spectra into their individual emission components
using a multi-component fitting approach. A complementary decomposition of the
spectra enables us to isolate the macro-lensed fraction of the spectra
independently of any spectral modelling.
  Results: -1. The data support micro-lensing de-amplification of images A and
C. Not only is the continuum emission microlensed in those images but also a
fraction of the Broad Line emitting Region (BLR).-2. Micro-lensing of a very
broad component of MgII emission line suggests that the corresponding emission
occurs in a region more compact than the other components of the emission line.
-3. We find evidence that a large fraction of the FeII emission arises in the
outer parts of the BLR. We also find very compact emitting region in the ranges
3080-3540 A and 4630-4800 A that is likely associated with FeII. -4. The OIII
narrow emission line regions are partly spatially resolved. This enables us to
put a lower limit of 110h^{-1} pc on their intrinsic size. -5. Analysis of MgII
absorption found in the spectra indicates that the absorbing medium is
intrinsic to the quasar, has a covering factor of 20%, and is constituted of
small clouds homogeneously distributed in front of the continuum and BLRs. -6.
Two neighbour galaxies are detected at redshifts z=0.10 and z=0.289. These
galaxies are possible members of galaxy groups reported at those redshifts.
