What is the hypothesis that continents have moved slowly away from there current locations?

Answer 1

It was called "Continental Drift" and was promptly (and rightly) dismissed as it proposed that the Continents were somehow plowing through the solid rock of the Oceanic crust, like ships through the liquid water of the ocean.

It took observations made by the US Navy during the 1950s (and kept classified secrets for many years), including volcanic activity of the midocean ridges, magnetic reversals in the Oceanic crust that were symmetric about the midocean ridges, and very deep ocean trenches. These showed that large moving plates existed in the earth's crust that transported both the Continents and sections of Oceanic crust in various directions.

Ultimately this provided a workable mechanism that replaced the rejected "Continental Drift" hypothesis with the Theory of Plate Tectonics.