Hi Andrei, if use a plane as the surface to deform and target it onto a sphere, it will generate a new sphere.

For a sphere you don't really need to use UnwrapCurve to make the base plane, just make a plane that has a 2 to 1 width to height ratio (2 times wider than it is tall). That will then match a sphere surface's general proportions which has a 360 degree circle around the width and a 180 degree arc for the height of it (that's the 2 to 1 ratio).

I've attached an example - the exact size of the base plane doesn't particularly matter, just its ratio of width to height. Here I just drew one with width = 20 and height = 10.

Note that the places that you pick on the base plane and on the target sphere are significant, they will control which edges match with each other and so that controls rotation of the shape. Check out here for some descriptions of the pick areas:
http://moi3d.com/forum/index.php?webtag=MOI&msg=4795.10
http://moi3d.com/forum/index.php?webtag=MOI&msg=4442.24

- Michael