  Massive black holes in galactic nuclei vary their mass M and spin vector J
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 black hole growth evolving contemporarily mass, spin modulus a and spin
direction. We discover the occurrence of two regimes. An early phase (M <~ 10
million solar masses) in which rapid alignment of the black hole spin direction
to the disk angular momentum in each single episode leads to erratic changes in
the black hole spin orientation and at the same time to large spins (a ~ 0.8).
A second phase starts when the black hole mass increases above >~ 10 million
solar masses and the accretion disks carry less mass and angular momentum
relatively to the hole. In the absence of a preferential direction the black
holes 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 black hole spin can increase up to a ~ 1 for very massive black holes (M >~
100 million solar masses), and its direction is stable over the many accretion
cycles. We discuss the implications that our results have in the realm of the
observations of black hole spin and jet orientations.
