Spin-up parameters s for different disc models (thin disc in dotted orange, MAD in solid lines) as a function of the BH spin parameter a. Similarly to the thin disc, a MAD counter-rotating (a < 0) disc causes the BH to spin down. Co-rotating (a > 0) thin discs will spin the BH up, unlike the MAD ones (due to loss of angular momentum to the jets). A special MAD case for very low spins (0 ≤ a < a_tr) shows a weak spin-up, but is less than the spin-up from thin discs.