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abstract: |
    Large low surface brightness galaxies have recently been found to be abundant in nearby galaxy clusters. In this paper, we investigate these ultra-diffuse galaxies (UDGs) in the six *Hubble* Frontier Fields galaxy clusters: Abell 2744, MACSJ0416.1$-$2403, MACSJ0717.5$+$3745, MACSJ1149.5$+$2223, Abell S1063 and Abell 370. These are the most massive ($1$–$3 \times 10^{15}~M_\odot$) and distant ($0.308
    < z < 0.545$) systems in which this class of galaxy has been yet discovered. We estimate the clusters host of order ${\sim}$200–1400 UDGs inside the virial radius ($R_{200}$), consistent with the UDG abundance halo-mass relation found in the local universe, and suggests that UDGs may be formed in clusters. Within each cluster, however, we find that UDGs are not evenly distributed. Instead their projected spatial distributions are lopsided, and they are deficient in the regions of highest mass density as traced by gravitational lensing. While the deficiency of UDGs in central regions is not surprising, the lopsidedness is puzzling. The UDGs, and their lopsided spatial distributions, may be associated with known substructures late in their infall into the clusters, meaning we find evidence both for formation of UDGs in clusters and for UDGs falling into clusters. We also investigate the ultra-compact dwarfs 