Splitting beehives allows us to increase our beehive numbers. This may not be the best way to split a hive, but there are times when it helps to know how to split a beehive without a queen.
Normally we would prepare a few queen cells before splitting, or, order some queens in cages. This allows one to split a beehive in such a way that a queen is almost ready to take over the splits.
Making splits and not adding queens purchased from low genetic diversity suppliers may cost you a few weeks egg-laying, but, it may allow you to begin to adapt your bees to your unique local conditions.