We explore modelling of super-massive galactic centres as horizon-less objects of degenerate neutron/proton/electron matter with no central singularity or surface-of-separation. Stable solutions to the radially-symmetric Einstein-Hilbert equations (Tolman form) have matter distributed in a shell of Schwarzschild scale (Rg), whose interior contains intense gravitational field energy. A typical solution for the SgrA* galactic centre (Rg =12 Gm) is a shell of radius 1.2 Rg, density peaking at 154 tonnes/cm3 and shell width 73 km. At such densities, the neutron fluid description is only marginally valid, with a fraction of the neutrons decaying to a proton and electron. We follow Weinberg’s analysis to obtain a modified Equation of State. This shows the fringes of the shell would be mainly Fermi gas of protons/electrons, with a transitional density of 29 tonne/cm3. Our galactic centre body is thus a hybrid between neutron- and electron- degenerate matter, while larger galactic centres have lower density shells and can be termed Supermassive White Giants (SWGs) analogous to traditional White Dwarfs. The trajectory of a test-particle entering the shell penetrates to a finite distance and then returns outwards, which is one indicator of stability. Matter accreted onto the shell would be quickly turned into degenerate ‘white dwarf’ material.