Then I think that in the long run the water would tend to move all the way to the poles draining drastically the remaining of the planet. If we think of an ocean as salty (3.5%) as ours, possibly there would be deposition of large layers of salt, most of it sodium chloride. I don't really know if there would be a "life zone" around some high latitude. Certainly tropic would have no meaning in this configuration.

That is the "big picture", but not all the story.

We have different wind flow in atmosphere and water flow in the oceans due to others factors. One of those being the tides that move water in waves half circumference of the planet. The main component being that from the moon, but we have other of smaller intensities like the solar influence. Other factors are the convection due difference temperatures and pressures, and Coriolis force making it go round in its trip across latitudes.

Another factor is that we have a non homogeneous distribution of mass on planet surface, the removal of large amount of water, moved to the poles, possibly would increase the amount of wobbling, then the precession ( https://en.wikipedia.org/wiki/Axial_precession) of the planet. Perhaps this wobbling would be responsible to a certain amount of melting at the poles, keeping the pumping working longer and, who knows, preserving some life in the planet.

A hotter atmosphere could increase the amount of clouds, if it covers all the planet we could have a very long freezing of the planet.

If we think on a dry planet with water moved to poles as ice, we could perhaps include sublimation of ice in the figure, adding the loss of water to space due to heating of the atmosphere. I don't think we would become a Mars, our gravity is about three times Mar's gravity.

HTH