Abstract Background Lamina-associated domains (LADs) are large genomic regions that are positioned at the nuclear lamina. It has remained largely unclear what drives the positioning and demarcation of LADs. Because the insulator protein CTCF is enriched at LAD borders, it was postulated that CTCF binding could position some LAD boundaries, possibly through its function in stalling cohesin and hence preventing cohesin invading into the LAD. To test this, we mapped genome–nuclear lamina interactions in mouse embryonic stem cells after rapid depletion of CTCF and other perturbations of cohesin dynamics. Results CTCF and cohesin contribute to a sharp transition in lamina interactions at LAD borders, while LADs are maintained after depletion of these proteins, also at borders marked by CTCF. CTCF and cohesin may thus reinforce LAD borders, but do not position these. CTCF binding sites within LADs are locally detached from the lamina and enriched for accessible DNA and active histone modifications. Remarkably, despite lamina positioning being strongly correlated with genome inactivity, this DNA remains accessible after the local detachment is lost following CTCF depletion. At a chromosomal scale, cohesin depletion and cohesin stabilization by depletion of the unloading factor WAPL quantitatively affect lamina interactions, indicative of perturbed chromosomal positioning in the nucleus. Finally, while H3K27me3 is locally enriched at CTCF-marked LAD borders, we find no evidence for an interplay between CTCF and H3K27me3 on lamina interactions. Conclusions These findings illustrate that CTCF and cohesin are not primary determinants of LAD patterns. Rather, these proteins locally modulate NL interactions.