Bonsoir, anyhow, when thinking about cartography and projections, the logical place is to that start reading about what it all entails. I spotted this http://www.progonos.com/furuti/MapPr...C/cartTOC.html on a link aggregate site today, and it's a cornucopia of cartography info.

The problem with what you want is that you want to transform a natively flat surface onto a sphere, while cartography is always about the opposite. You can't do it without stretching or wrinkles: imagine if you took a piece of paper and tried to wrap it around a balloon: you could make a cylinder, but not a curved surface easily. But your world is not made out of paper, it's made out of soil, rock, maybe lava, and water, so what I'd do is try stretching. If you want to do it "realistically", the result would also involve some breaking, so pieces would break apart, mimicking some tectonic processes.

If you want to do it mythically or magically (though it wouldn't hurt a myth to have huge rifts all over the place), I'm not really sure how you'd go about it. The simplest would be just map your basic map onto a circular projection, and then use that as the base by "reversing" the transformation into some other projection.

Long story short, there is no obvious way to do this. What scale are you thinking? Will this continent cover half the globe?