“…The interest towards central spin models has remarkably grown thanks to: I) their suitability in describing the hyperfine interaction in quantum dots [27] and the interactions between nuclear spins and nitrogen-vacancy centers in diamond [28,29] ; II) their broad applicability in different fields like quantum information, [30] quantum metrology and sensing, [31,32] quantum thermodynamics [33] and fundamental aspects. [34] Further, a lots of works have been developed to investigate the quantum correlation and thermal entanglement arising among spins in the star framework, [35][36][37][38][39] as well as the Markovian and non-Markovian dynamics induced by a surrounding bath interacting with the spinstar system. [40][41][42] Recently, the idea of spin-chain-star system has been proposed [43,44] where the control spin occupies the center of a star of M rays (chains), arranged at angular distance 2𝜋∕M, each of which hosts the same sequence of N spins, generally equidistant.…”