The binary and ternary cold fragmentations of heavy nuclei are studied in t
he framework of a deformation-dependent cluster model in which the final fr
agments are produced in their respective ground states and interact via a d
ouble-folded potential with M3Y forces. The deformation effects are taken i
nto account up to multipolarity lambda=4. It is shown that two regions of c
old fragmentation arise. The first one has large quadrupole and even hexade
capole deformations and mass number of the heavy fragment ranging between 1
38 and 158. In the second region, the Q-value principle dictates the occurr
ence of a few spherical nuclei around the doubly magic nucleus Sn-132, whic
h is similar to the case of heavy-cluster radioactivity, where the daughter
nuclei are around Pb-208. This structure is similar for binary and ternary
cold fission. The cold-fission yields are computed for the binary fragment
ation and for the alpha-accompanied fission of Cf-252. For the ternary cold
-fission mode we derive the most likely geometrical and dynamical character
istics of the fragments at the moment of release of the light particle and
perform classical trajectory calculations, in order to compute the final ki
netic energy of the alpha particle. The recent observation of Be-10 in cold
ternary fission is discussed in connection with the concept of a giant nuc
lear molecule. (C) 1999 American Institute of Physics. [S1063-7796(99)00304
-6].