Hi, I have been researching the single brood box concept. I would suggest you google "single brood box management". You will see videos that will help explain. The University of Guelph in Ontario has some interesting information. I plan on either using 1 deep or 1 deep and 1 medium for brood in a couple of hives to try this summer. The main difference with a single brood box is that as soon as the Queen starts to expand the hive it is necessary to install a Queen excluder and supers. This will allow the bees to expand to the top boxes and not be so crowded that the Queen decides to swarm. Another benefit is that there is only one deep box to inspect. According to one of the videos there are ample cells available in a single deep to allow the Queen to lay as many eggs as she wants. By the time the cells get anywhere near full there is emerging brood making room for new eggs.
As a side note, I have been using 3 deeps for several years, to insure that there was ample room and the Queen would not swarm (among other factors, slatted rack, ventilation collars etc). Last Summer I lost 2 hives to Small Hive Beetles, weak, smaller hives and I usually did not inspect the lowest box. Big mistake, the SHB took over and it was not good. Check out the Videos.