Mechanism behind ocean-containing ice caps

I don't fully understand the mechanisms behind an ice cap that contains all the water in the oceans. Just to be specific, I have a planet that resembles Mars, i.e. desert at the equator, ice at poles. I want the equator to be hot, but the ice caps to contain the entirety of the oceans.

I really like super detailed information, so I want to know, how would the oceans migrate towards the poles and eventually get stuck there forever, with the equator still managing to be hot?

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Mechanism behind ocean-containing ice caps

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