In Lambda-CDM models, galaxies are thought to grow both through continuous cold gas accretion coming from the cosmic web and episodic merger events. The relative importance of these different mechanisms at different cosmic epochs is nevertheless not yet understood well. We aim to address questions related to galaxy mass assembly through major and minor wet merging processes in the redshift range 1 < zeta < 2, an epoch that corresponds to the peak of cosmic star formation history. A significant fraction of Milky Way-like galaxies are thought to have undergone an unstable clumpy phase at this early stage. We focus on the behavior of the young clumpy disks when galaxies are undergoing gas-rich galaxy mergers. The star formation history of isolated disks shows a stochastic star formation rate, which proceeds from the complex behavior of the giant clumps. The mass-size relation and its rate of evolution in the redshift range 1 < zeta < 2 matches observations, suggesting that the inside-out growth mechanisms of the stellar disk do not necessarily require cold accretion.