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There is strong observational evidence that many active galactic nuclei (AGNs) harbour super-massive black holes (SMBHs), demonstrating multi-accretion episodes during their life-time. In such AGNs, corotating and counterrotating tori, or strongly misaligned disks, as related to the central Kerr SMBH spin, can report traces of the AGNs evolution. Here we concentrate on aggregates of accretion disks structures, ringed accretion disks (RADs) orbiting a central Kerr SMBH, assuming that each torus of the RADs is centered in the equatorial plane of the attractor, tori are coplanar and axi-symmetric. Many of the RAD aspects are governed mostly by the spin of the Kerr geometry. We classify Kerr black holes (BHs) due to their dimensionless spin, according to possible combinations of corotating and counterrotating equilibrium or unstable (accreting) tori composing the RADs. The number of accreting tori in RADs cannot exceed n = 2. We present list of 14 characteristic values of the Kerr BH dimensionless spin a governing the classification in whole the black hole range 0 <= a <= M, uniquely constrained by the RAD properties. The spin values are remarkably close providing an accurate characterization of the Kerr attractors based on the RAD properties. RAD dynamics is richer in the spacetimes of high spin values. One of the critical predictions states that a RAD tori couple formed by an outer accreting corotating and an inner accreting counterrotating torus is expected to be observed only around slowly spinning (a < 0.46 M) BHs. The analysis strongly binds the fluid and BH characteristics providing indications on the situations where to search for RADs observational evidences. Obscuring and screening tori, possibly evident as traces in x-ray spectrum emission, are strongly constrained, eventually ruling out many assumptions used in the current investigations of the screening effects. We expect relevance of our classification of Kerr spacetimes in relation to astrophysical phenomena arising in different stages of AGNs life that could be observed by the planned x-ray satellite observatory ATHENA (Advanced Telescope for High ENergy Astrophysics).