  The simplest cuprate superconductor La2CuO4+y with mobile oxygen
interstitials exhibits a clear phase separation, but only recently a bulk
multiscale structural phase separation has been observed by using scanning
micro X-ray diffraction. Here we get further information on the structural
phase separation, using local probe X-ray absorption near edge structure. The
spatial distribution of superconducting units is a key parameter controlling
percolative superconductivity in complex matter with dispersed superconducting
units. These oxides form super-molecular architectures made of superconducting
atomic monolayers intercalated by spacers. Oxygen interstitials enter into the
rocksalt La2O2+y spacer layers forming oxygen interstitials rich puddles and
poor puddles. Their spatial distribution has been determined by using scanning
La L3-edge micro X-ray absorption near edge structure. Percolating networks of
oxygen rich puddles are observed in different micrometer size portions of the
crystals. Moreover, the complex surface resistivity shows two jumps associated
to the onset of intra-puddle and inter-puddles percolative superconductivity.
The similarity of oxygen doped La2CuO4+y, with the well established phase
separation in iron selenide superconductors is also discussed.
