Ocean iron fertilization (OIF) aims to remove carbon dioxide (CO2) from the atmosphere by stimulating phytoplankton carbon-fixation and subsequent deep ocean carbon sequestration in iron-limited oceanic regions. Transdisciplinary assessments of OIF have revealed overwhelming challenges around the detection and verification of carbon sequestration and wide-ranging environmental side-effects, thereby dampening enthusiasm for OIF. Here, we utilize five requirements that strongly influence whether OIF can lead to atmospheric CO2 removal (CDR): The requirement (a) to use preformed nutrients from the lower overturning circulation cell; (b) for prevailing iron-limitation; (c) for sufficient underwater light for photosynthesis; (d) for efficient carbon sequestration; (e) for sufficient air-sea CO2 transfer. We systematically evaluate these requirements using observational, experimental, and numerical data in an "informed back-of-the-envelope approach" to generate circumpolar maps of OIF (cost-)efficiency south of 60 degrees S. Results suggest that (cost-)efficient CDR is restricted to locations on the Antarctic Shelf. Here, CDR costs can be <100 US$/tonne CO2 while they are mainly >>1,000 US$/tonne CO2 in offshore regions of the Southern Ocean, where mesoscale OIF experiments have previously been conducted. However, sensitivity analyses underscore that (cost-)efficiency is in all cases associated with large variability and are thus difficult to predict, which reflects our insufficient understanding of the relevant biogeochemical and physical processes. While OIF implementation on Antarctic shelves appears most (cost-)efficient, it raises legal questions because regions close to Antarctica fall under three overlapping layers of international law. Furthermore, the constraints set by (cost-)efficiency reduce the area suitable for OIF, thereby likely reducing its maximum CDR potential.