The northern and southern hemispheres of Mars are differentiated by both topology and elevation. The southern hemisphere is characterized by highlands (relative to the northern hemisphere), the surfaces of which are called chaoses. They are called chaoses becuse of a fantastic mix of teatures, perhaps the most interesting being evidence of ancient liquid water, the flow channels of which just simply stop, for no discernible reason. The rest of the surface is characterized by cratering, ancient volcanism, uplift features that resemble pingoes, but on the gigantic Martian scale--in short, characterized by having no single characteristic features.
There is a feature known as the Xanthe Terra which "sticks up" out of the southern chaoes, across the equator into the northern hemisphere. The southern end of this feature has the features of the southern chaoses, but the northern end of the Xanthe Terra is strikingly different. It shows the most prominent evidence of flowing water on the planet. Huge channels and vast alluvial fans. The flow which would have created them are, like everyihing else on Mars, on a gigantic scale--perhaps as much as 10,000 times the flow of the Mississippi-Missouri-Ohio drainage in North America.
Where would that water have gone? Downhill of course, to what is known as the Vastitas Borealis (northern wilderness or northern wasteland).
Competing hypotheses are often cudgels with which scientists belabor one another. I don't think it has reached that point with areology yet, but that's mostly because of a lack of data. There are two camps on the subject of liquid water on Mars. One is the long wet period and the other (unsurprisingly) the short wet period. The proponents of the long wet period hypothesize an ocean in the northern hemisphere called the Oceanus Borealis. Below is an artist's rendering:
Those who support the hypothesis point to the uniform surface of the Vastitas Borealis, as evidence of an ancient sea bed (there are problems with this, though). They also point to evidence of what they say are ancient shorelines along the edges of the higher elevations in the northern hemisphere, which are all just north of the equator. The supporters of this hypothesis say that the features of the Vastitas Borealis are consistent with a sea bed.
But there the controversy begins. Those who favor the short wet period point out the features of the Vastitas which are not consistent with a sea bed. There are large boulders on the plain of the Vastitas, and they could not have been carried there by water. There are also features which some researchers say resemble eskers, the saying of which is convenient to their hypothesis. They allege that the northern half of the northern hemisphere was once covered by vast glaciation (on a typically Martian gigantic scale), which would account for the boulders and the eskers, if eskers they are. Proponents of this point of view contend that there was a very brief period when the glaciers melted, leaving the eskers behind. They are content that their hypothesis covers the data. The Red Planet Report
states the the surface penetrating radar now in use tends to confirm the Oceanus Borealis hypothesis--without, however, resolving the completing claims of the long wet period group or the short wet period group.
Just to muddy the waters, as scientists love to do, there is the episodic hypothesis, which you can read about in this PDF document, which is an abstract.