A method to increase colony numbers
"Walk away split" is an American term for splitting a colony and leaving it to raise its own queen. There are a number of ways of achieving this, but in simple terms a strong colony is split into two, with one part retaining the queen, the other part having eggs and young larvae from which the bees raise a queen by building emergency cells.
In the simplest form, and probably what happened originally, the two colonies are left alone for 4 weeks, after which the queenless part should have a laying queen, hence "walk away split".
By consulting literature or looking online you will find there are almost as many methods (and arguments!) as there are beekeepers. Some will simply split a colony into two, making sure both parts have eggs and young larvae. They don't even bother to find the queen, as they know that both parts are able to raise one from existing larvae. Other beekeepers will do it in a more controlled way, which probably gives better results.
It doesn't seem to matter which part goes where. Some beekeepers move one part right away to another apiary, others keep both parts in the same apiary. Likewise, some put the part with the queen on the old stand, some put the part without the queen.
This simple method of increase has been used for a very long time. With little effort and cost it increases colony numbers and produces new queens to head them. When I started beekeeping in 1963 in Sussex, it was soon after the hard 1962/63 winter when many colonies were lost. Many beekeepers had good practical skills, but little knowledge. They had many hives to re-populate, so apart from catching and hiving swarms, this was their main method of making increase, but the term "walk away split" wasn't used.
I believe that walk away splits are more likely to be successful in countries where the climate is good, the foraging season long and the bees prolific, as in the U.S. If done early in the season, this gives both colonies the chance to build up quickly, so they both get a honey crop. We don't often get those conditions in the U.K. so I think this method is unlikely to be so successful.
If anyone wishes to try it, I suggest leaving the queenless part on the old stand, so they retain the flying bees, making a stronger colony that will probably produce better queen cells. I would remove all queen cells bar one 8-9 days after splitting to prevent them swarming. This puts more control into the operation but takes away the meaning of "walk away split". It is also little different from an artificial swarm.
Although largely successful I prefer to use a more managed way of making increase, if possible by rearing queens from selected stock, so you don't rely on emergency cells.