We investigate whether the Hubble sequence can be reproduced by the relics of merger events. We verify that, at z_median = 0.65, the abundant population of anomalous starbursts - i.e. with peculiar morphologies and abnormal kinematics - is mainly linked to the local spirals. Their morphologies are dominated by young stars and are intimately related to their ionised-gas kinematics. We show that both morphologies and kinematics can be reproduced by using gas modelling from Barnes' (2002, MNRAS, 333, 481) study of major mergers. Their gas content may be indirectly evaluated by assuming that distant starbursts follow the Kennicutt-Schmidt relation: the median gas fraction is found to be 31%. Using our modelling to estimate the gas-to-star transformation during a merger, we identify the gas fraction in the progenitors to be generally above 50%. All distant and massive starbursts can be distributed along a temporal sequence from the first passage to the nuclei fusion and then to the disk rebuilding phase. This later phase has been recently illustrated for J033245.11-274724.0, a distant compact galaxy dominated by a red, dust-enshrouded disk. This active production of rebuilt disks is in excellent agreement with model predictions for gaseous rich encounters. It confirms that the rebuilding spiral disk scenario - a strong and recent reprocessing of most disks by major mergers - is possibly an important channel for the formation of present-day disks in grand-design spirals. Because half of the present-day spirals had peculiar morphologies and anomalous kinematics at z_median = 0.65, they could indeed have been in major merger phases 6 Gyr ago, and almost all at z ~ 1. It is time now to study in detail the formation of spiral disks and of their substructures, including bulge, disks, arms, bars and rings that may mainly originate from instabilities created during the last major merger. Many galaxies also show a helicoidal structure, which is probably due to a central torque, and seems to play an important role in regulating the angular momentum of the newly-formed disks.

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