Massive black holes (BHs) in galactic nuclei vary their mass M BH and spin vector J BH due to accretion. In this study we relax, for the first time, the assumption that accretion can be either chaotic, i.e., when the accretion episodes are randomly and isotropically oriented, or coherent, i.e., when they occur all in a preferred plane. Instead, we consider different degrees of anisotropy in the fueling, never confining to accretion events on a fixed direction. We follow the BH growth evolving contemporarily with mass, spin modulus a, and spin direction. We discover the occurrence of two regimes. An early phase (M BH 107 M ☉) in which rapid alignment of the BH spin direction to the disk angular momentum in each single episode leads to erratic changes in the BH spin orientation and at the same time to large spins (a ~ 0.8). A second phase starts when the BH mass increases above 107 M ☉ and the accretion disks carry less mass and angular momentum relative to the hole. In the absence of a preferential direction, the BHs tend to spin-down in this phase. However, when a modest degree of anisotropy in the fueling process (still far from being coherent) is present, the BH spin can increase up to a ~ 1 for very massive black holes (M BH 108 M ☉), and its direction is stable over the many accretion cycles. We discuss the implications of our results in the realm of the observations of BH spin and jet orientations.
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