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The mass assembly in star-forming regions arises from the hierarchical structure in molecular clouds in tandem with fragmentation at different scales. In this paper, we present a study of the fragmentation of massive clumps covering a range of evolutionary states, selected from the ATLASGAL survey, using the compact configuration of the Submillimeter Array. The observations reveal a wide diversity in the fragmentation properties with about 60% of the sources showing limited to no fragmentation at the 2″ scale, or a physical scale of 0.015–0.09 pc. We also find several examples where the cores detected with the Submillimeter Array are significantly offset from the clump potential, suggesting that initial fragmentation does not result in the formation of a large number of Jeans mass fragments. The fraction of the clump mass that is in compact structures is seen to increase with source evolution. We also see a significant correlation between the maximum mass of a fragment and the bolometric luminosity of the parent clump. These suggest that massive star formation proceeds through clump fed core accretion, with the initial fragmentation being dependent on the density structure of the clumps and/or magnetic fields.