Research over the past decade has shown diminishing empirical evidence for major galaxy mergers being a dominating or even important mechanism for the growth of supermassive black holes in galaxies and the triggering of optically or X-ray selected active galactic nuclei (AGN). We here for the first time test whether such a connection exists at least in the most plausible part of parameter space for this mechanism: the highest specific accretion rate broad-line AGNs at the peak epoch of black hole activity around z = 2. To that end we examine 21 galaxies hosting a high accreting black hole (L/Ledd > 0.7) observed with HST/WFC3 and 92 stellar mass- and redshift- matched inactive galaxies taken from the CANDELS survey. We removed the AGN point sources from their host galaxies and avoided bias in visual classification by adding and then subtracting mock point sources to and from the comparison galaxies, producing matched residual structures for both sets. The resulting samples were joined, randomized, and subsequently visually ranked with respect to perceived strength of structural distortions by 10 experts. The ensuing individual rankings were combined into a consensus sequence and from this we derived merger fractions for both samples. With the merger fractions f$_{m,agn}$ = 0.24 $pm$ 0.09 for the AGN host galaxy sample and f$_{m,ina}$ = 0.19 $pm$ 0.04 for the inactive galaxies, we find no significant difference between the AGN host galaxies and inactive galaxies. Also, both samples display comparable fractions of disk-dominated galaxies. These findings are consistent with previous studies for different AGN populations, and we conclude that even black hole growth at the highest specific accretion rates and at the peak of cosmic AGN activity is not predominantly caused by major mergers. (abriged)
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