they seem to split when changes in their environment occur. for example, each time i've moved mine have split. i've heard of people keeping them in prop tanks and shifting the salinity to get them to split. seems to be a survival mechanism. i've also heard of people splitting them with razor blades. i know calfo talked to some members about that. maybe they can elaborate as i was not in attendance.
The info on splitting BTAs is great. I've been attempting similar approaches with other anenomes with little succuss. A sebae with a diameter of about 8-10 inches received an incision approx. 1.5 inches into the disc. The incision healed and over time, it has filled in the v-shaped injury and will eventually no longer be visible. I've tried other methods with no success. I guess I have the wrong type of anenome.
The combination of environmental change and overfeeding often results in splitting without having to cut the animal. I almost accidently caused my RTBA to split by feeding her daily after putting her in my tank... There is an excellent FAQ out there though I'm having trouble locating it. I would imagine there is varience between species too.
Basically either way involves stressing the animal (not unlike child birth)