In order to better describe both ancient and contemporary migratory flows associated with the North Atlantic abyssal fauna as part of the EC H2020 iAtlantic project, this dataset provides a collection of connectivity maps for several engineer species from hydrothermal springs on the Mid-Atlantic Ridge, from mussels of cold seeps on both sides of the Atlantic and, from deep-water corals in the NE Atlantic. These maps and the associated migrant flow matrices are derived from several demogenetic model analyses (dadi, moments and divmigrate) using multi-locus genotype data derived from a sub-sampling of the genomes of these target species. For each species, the dataset includes a series of shapefiles with a pdf map, the file of the geographic coordinates of the studied localities with a flow matrix, as well as the file of the multi-locus genotypes used to carry out the genetic analysis of the populations and establish the migratory flows.