Black hole dimensionless spin χ_BH as a function of the He-rich star mass and the orbital period. The black symbols represent the initial parameters (He-rich star mass and orbital period), and the colored symbols indicate the final parameters. The color gradient along the line traces the evolution of χ_BH, assuming that the He-rich star collapses directly into a BH without losing mass or angular momentum. The triangles represent BNS systems, circles denote NSBH systems, stars indicate dynamical delayed instability (DDI), and crosses mark initial overflow cases. The three columns correspond to different metallicities (left: 1.0 Z_⊙; middle: 0.1 Z_⊙; and right: 0.01 Z_⊙). The plus symbol refers to the systems that might be representative of the progenitors of GW230529.