The ternary cluster decay of heavy nuclei (e.g. in spontaneous fission of 252 Cf(sf,fff)), has been observed in several experiments with binary coincidences between two fragments using detector telescopes (the FOBOS-detectors) with very large solid angles and placed on the opposite sides from the source of fissioning nuclei. The binary coincidences at a relative angle of 180 0 deg. correspond to binary fission or to the decay into three cluster fragments by registration of two of them in coincidences with missing nuclei of different masses (e.g. 132 Sn, 52−48 Ca, 68−72 Ni). This marks a new step in the physics of fission-phenomena of heavy nuclei. The new decay mode has been observed more then 10 years ago by the FOBOS group in JINR (Dubna) Russia. These experimental results for the collinear cluster tripartition (CCT), refer to the decay into three clusters of comparable masses. In the present work we discuss the various aspects of this ternary fission (FFF) mode, with different mass partitions.The question of collinearity is analysed on the basis of recent publications. Further insight into the possible decay modes is obtained by the discussion of the path towards larger deformation, towards hyper-deformation and by inspecting details of the potential energy surfaces (PES). The PES is determined as the total sum of the masses, including the shell effects, which enter with Qggg, the three-body Q-value for the separation into three fragments, and the total interaction (nuclear and Coulomb) between all three nuclei. In the path towards the extremely deformed states leading to ternary fission, the concept of deformed shells is most important. At the scission configuration the phase space determined by the PES's leads to the final mass distributions. The possibility of formation of fragments of almost equal size (Zi = 32, 34, 32, for Z=98) and the observation of several other fission modes in the same system can be predicted by the PES. The PES's show pronounced minima and valleys, where the phase space for the decay reaches maximum values, namely for several mass/charge combinations of ternary fragments, which correspond to a variety of collinear ternary fission (multi-modal) decays. The case of the decay of 252 Cf(sf,fff) turns out to be unique due to the presence of deformed shells in the total system and of closed shells in all three nuclei in the decay.