Small basin studies in the remote Canadian Arctic Archipelago have revealed the general nature of runoff processes and the annual rhythms and magnitude of streamflow in the region. Widespread monitoring of hydrological cycle components is absent even though such understanding is important for sound domestic water management decisions and international obligations to quantify Canada’s freshwater supply to the oceans. The authors extrapolated observed streamflow attributes, including the date of the spring maximum, across the Arctic Archipelago using statistical regionalization tools. The paucity of hydrometric data necessitated the construction of a dataset, which was limited to the period from 1972 to 1994. Reliable estimates of mean May to October freshwater flux were possible from ~70% of the Archipelago and these total ~190 km³. Flows were highest from southern Baffin Island, decreasing westward. Spring maximum flows begin in the southwest and proceed northeasterly. The scarcity of data compelled an error analysis that showed average confidence intervals around constructed and regionalized data of ±123% and ±63%, respectively. Dataset construction errors were inversely related to basin area. There was no spatial pattern to the dataset construction errors, but regionalization error tended to be higher in the west. It will be argued that our community has little to no idea of the current freshwater flux from the Arctic Archipelago, or how it could be changing.