The phrase “shallow epicontinental seas” only comes up when talking about one specific subject: the Cretaceous period, and the many swimming dinosaurs that inhabited them, such as mosasaurs. Imagine a 50-foot-long crocodile with giant flippers that glides like a whale and eats anything. It would even eat your hairy nutsack after you’ve been wrestling. Even that.
The shallow epicontinental seas existed due to higher-than-normal sea levels during the cretaceous period (possibly caused by caveman fires which created global warming or something, I forget my natural history). This caused the continental lowlands to flood for thousands and thousands of miles. Whole ecosystems were supported by these expansive shallow epicontinental seas, and creatures such as the mosasaur were the top predators within.
The Persian Gulf, the North Sea, and even Hudson Bay are considered to be extant shallow epicontinental seas.