Decomposing the growth mechanisms of galaxies over the last 10 billion years

Determining how galaxies accumulate stellar mass is paramount to understanding the Universe. Two primary mechanisms drive this process: star-formation (SF) & mergers. Our understanding of star formation, and to some degree the processes that influence the baryon cycle (environment, gas supply, feedback, etc), are either relatively well constrained or will develop significantly over the coming decades via upcoming facilities (i.e. through their imprint on galaxy properties measured with deep multi-wavelength and spectroscopic data). However, the same can not be said for mergers. It is telling that we indirectly know hierarchical assembly through mergers is one of the most crucial processes that shape our Universe, but the robust observational measurement of mergers is almost non-existent outside of the local Universe - let alone how these mergers impact galaxy properties. This is not likely to significantly change in the coming decades as existing or approved facilities/surveys are inadequate in charactering mergers in the distant Universe. Motivated by this, we discuss an ambitious study to first explore mergers, and then the co-dependent astrophysical process that govern the accumulation of stellar mass over the last ~10billion years, and highlight the essential need for a 10m+ class multi-object spectroscopic facility.