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Our understanding of the formation and evolution of binary black holes (BBHs) is significantly impacted by the recent discoveries made by the LIGO/Virgo collaboration. Of utmost importance is the detection of the most massive BBH system, GW190521. Here we investigate what it takes for field massive stellar binaries to account for the formation of such massive BBHs. Whether the high mass end of the BH mass function is populated by remnants of massive stars that either formed at extremely low metallicities and avoid the pair-instability mass gap or increase their birth mass beyond the pair-instability mass gap through the accretion of gas from the surrounding medium. We show that assuming that massive stars at very low metallicities can form massive BHs by avoiding pair-instability supernova, coupled with a correspondingly high formation efficiency for BBHs, can explain the observed BH mass function. To this end, one requires a relation between the initial and final mass of the progenitor stars at low metallicities that is shallower than what is expected from wind mass loss alone. On the other hand, assuming pair-instability operates at all metallicities, one can account for the observed BH mass function if at least about 10% of the BHs born at very low metallicities double their mass before they merge because of accretion of ambient gas. Such BBHs will have to spend about a Gyr within a parsec length-scale of their parent atomic cooling halos or a shorter timescale if they reside in the inner sub-parsecs of their host dark matter halos. Future stellar evolution calculations of massive stars at very low metallicity and hydrodynamical simulations of gas accretion onto BBHs born in atomic cooling halos can shed light on this debate.