How Fast do Black Holes Spin?

We present a systematic study of the spin evolution of accreting black holes. Using the BHAC code for general relativistic magnetohydrodynamic simulations, we conduct a total of 500 high resolution simulations of magnetized accretion disks around Kerr BHs with spin parameters ranging from $χ=0$ to $χ= 0.99$. The baseline configuration follows the default Fishbone--Moncrief torus setup in BHAC. We further explore the effects of: I) introducing multiple poloidal magnetic loops, II) the initial position of the torus, III) magnetic field strength and IV) radial loop modulation. From each simulation we extract the mass flux and angular momentum flux through the horizon to compute the time-averaged spin evolution rate after the system becomes quasi-stationary. The equilibrium spin ranges from $χ_{\rm eq}\simeq0.88$ in the fiducial model to $χ_{\rm eq}\simeq0.98$ for weak-flux model. Applied to Sgr A$^*$, even an optimistic estimate for rapid spin evolution gives a timescale longer than $10^{13}$ yr, indicating an earlier growth or merger history. These trends are consistent with the picture that larger net magnetic flux threading the horizon enhances jet-torques and reduces the equilibrium spins, whereas weak net flux yields near-maximal spins. Our results provide a pathway to interpret the high spins reported for X-ray binaries and active galactic nuclei and they sharpen the astrophysical viability of near-horizon high-energy processes that rely on near-extremal black holes.