You usually create partition wall corners from 2-by-4s, boards 2 inches wide and 4 inches deep. You then cut them to length depending on the height of the wall. But you might have to make a corner out of another size of dimensional lumber. For instance, 2-by-6s, boards that measure 2 inches deep and 6 inches wide, might be needed when framing partition walls that contain certain features, such as plumbing pipes.
When a partition wall meets another wall at a corner, the established practice is to create a corner post. The post will contain more wood than the single studs that builders use to create the body of a wall. A single stud at a corner does not provide enough backing for the drywall that will go on after that framing has finished. The extra wood adds strength to the wall and provides the width necessary to support the drywall that will cover the corner.
The three-stud framing method, a standard method for creating a partition wall corner post, provides a solid corner and adequate backing for applying drywall, according to the Extreme How-To website. Nail three studs together with 16d nails, driving them flush with the surface of the wood. Space the nails 16 inches apart. The usual method of building the corner is to frame the partition wall and the corner post on the floor, and then raise it into position after it's assembled.
In some cases, such as when you need to run electrical cable through a corner post, the three-stud approach might not work well. A better plan involves the use of blocking, smaller pieces of wood that are the same dimension as the studs. Use two studs for the exterior of the post, and fill in the spaces between them with blocking. Leave some empty space between the pieces of blocking for the cables to pass through.