[en] A long-standing theoretical change is predictions of optimum incident systems, optimum incident energies, as well as those of maximum residue cross sections for synthesis of super-heavy elements (SHE). Theoretical predictions, however, have ambiguities stemming from two causes: unknown masses or shell correction energies (SCE) of SHE nuclei themselves and unexplained mechanism of the fusion hindrance, experimentally known since many years ago. On the former, there are rather precise predictions by structure studies, but they are different with each other, so predicted SCE's are not reliable precisely, because 1 MeV difference in them results in change in residue cross section about one order of magnitude through so-called survival probability (It should be noted that fission barrier of SHE is given totally by SCE). On the latter, there was no reaction theory encompassing the hindrance mechanism. The present authors have proposed the two-step model for the fusion process, which explains the hindrance qualitatively [1], and which is applicable to the cold as well as to the hot fusion paths [2]. However, the model overestimates the absolute values of the cross sections, if the masses predicted by P. Moeller et al. [3] are used. Examples of the calculated excitations are shown in Fig. 1 [4] and 2, with only one free parameter f, a factor for SCE, in order to reproduce order of magnitude of the cross sections. As for the formation step of the spherical compound nucleus, the present authors recently have made a closer analysis of fusion dynamics from di-nucleus to mono-nucleus, which improves predictions of fusion probability quantitatively [5]. That is expected to make a free parameter f to be unnecessary to introduce. Furthermore, the neck dynamics is found to depend on mass-asymmetry and thus, fusion probability depends on incident channel with the neck dynamics unknown so far. In connection with the question on which path is more favorable when we proceed to heavier systems, the compound nucleus with Z=120 is an interesting object to study theoretically, because there are three incident systems with different mass-asymmetry. Experiments are under way or are expected to be made in a near future. Theoretical predictions obtained with the refinements by the neck dynamics will be reported for heavier elements not yet measured.(author)