We consider a star-network of n=n0+np spin-1/2 particles, where interaction between n0 central spins and np peripheral spins are of the XYZ-type. In the limit n0/np << 1, we show that for odd n, the ground state is doubly degenerate, while for even n, the energy gap becomes negligible when n is large, inducing an effective double degeneracy. In the same limit, we show that for vanishing xy-anisotropy, bipartite entanglement on the peripheral spins computed using either a partial trace-based, or a measurement-based approach exhibits a logarithmic growth with np, where the sizes of the partitions are typically ~ np/2. This feature disappears for non-zero xy-anisotropy, which we refer to as the anisotropy effect. Interestingly, when the system is taken out of equilibrium by the introduction of a magnetic field of constant strength on all spins, the time-averaged bipartite entanglement on the periphery at the long-time limit exhibits a logarithmic growth with np irrespective of the value of xy-anisotropy parameter. We further study the n0/np >> 1 and n0/np -> 1 limits of the model, and show that the behaviour of bipartite peripheral entanglement is qualitatively different from that of the n0/np << 1.

https://arxiv.org/abs/2307.15949