Inside corner (a partition intersecting a wall) or outside corner?
Inside corners are formed with a partition post (p-post) or a set of ladder blocks. Ladder blocks are less material-intensive, which is important to me when studs are running as much as they are these days. You end up saving one or two studs per corner by using ladder blocks.
A p-post is a pair of 2x4's separated by either a full 2x4 on the flat or a gang of several cutoff scraps, in either case held flush with the edges of the principal 2x4's to form a C in section, with the solid back of the C facing the adjoining partition; this gives nailing for the partition, and both sides of the inside corners.
Ladder blocks are fit between common studs and are positioned every 2 feet down from the ceiling; they are nailed on flat to the wall plane, so they can be insulated behind and give a nice thermal break on outside walls, and allow the partition the be positioned at any point between the common studs. A line struck with the aid of a plumb bob or level so that the partition is plumb. Ladders are made from culls or cutoffs, and are essentially free.
An outside corner must always use a corner post. In 2x4 construction this is two studs with a row of cutoff scrap between for spacers; then, a third 2x4 of the adjoining wall is spiked into them when that wall is erected, giving full nailing for the inside of the corner and a fully-backed outside surface for the drywall or sheathing.
With 2x6 construction, this changes because one row of filler isn't enough to equal a 2x6's width. You can use some 2x4's sideways-oriented to gain the needed bulk. "California corners" are IMO to be avoided, except in attics where one side of an inside corner remains unfinished, but it's still quite inferior, and will often lead to the drywall seam cracking along the corner.
Remove not the ancient landmark, which your fathers have set.