The multinucleon transfer reactions near barrier energies has been investigated with a multistep model based on the dinuclear system (DNS) concept, in which the capture of two colliding nuclei, the transfer dynamics and the de-excitation process of primary fragments are described by the analytical formula, the diffusion theory and the statistical model, respectively. The nucleon transfer takes place after forming the DNS and is coupled to the dissipation of relative motion energy and angular momentum by solving a set of microscopically derived master equations within the potential energy surface. Specific reactions of $^{40,48}$Ca+$^{124}$Sn, $^{40}$Ca ($^{40}$Ar, $^{58}$Ni)+$^{232}$Th, $^{40}$Ca ($^{58}$Ni)+$^{238}$U and $^{40,48}$Ca ($^{58}$Ni) +$^{248}$Cm near barrier energies are investigated. It is found that the fragments are produced by the multinucleon transfer reactions with the maximal yields along the $beta$-stability line. The isospin relaxation is particularly significant in the process of fragment formation. The incident energy dependence of heavy target-like fragments in the reaction of $^{58}$Ni+$^{248}$Cm is analyzed thoroughly.
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