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In the field of paleoceanographic modeling, the different positioning of Earth’s continental configurations is often a major challenge for obtaining equilibrium ocean flow solutions. In this paper, we introduce numerical parameter continuation techniques to compute equilibrium solutions of ocean flows in the geological past, where we change the continental geometry and allow the flow to deform using a homotopy parameter. The methods are illustrated by computing equilibrium three-dimensional global ocean circulation patterns over the last 65 Ma under a highly idealized atmospheric forcing. These results already show interesting major transitions in ocean circulation patterns due to changes in ocean gateways, that may have been relevant for Cenozoic climate transitions. In addition, the techniques are shown to be computationally efficient compared to the established continuation spin-up approach. [ABSTRACT FROM AUTHOR]