Walls and Ceilings - door jamb larger then 2x4?

i bought a pre hung door from home depot for my basment remodeling project. ive set the door up in the rough opening, and ive noticed that the jamb hangs over the wall frame by a 1/2" on each side, since its 4 1/2" in width and obviously the studs are 3 1/2" stock

it seems logical to use 1/2" sheetrock all the way over to the jamb, which would make an even surface for the molding to go on.

am i wrong in assuming this? also what happens if you want to use 3/8" or even 5/8" sheetrock? how do you make the surface even for molding?

If you use 3/8 then you would have to rip the jam or shim the walls for 5/8 you would add 1/2 inch of wood to side of jam.