I have never seen a orange / yellow branching sun coral, but the brown / black ones I have are branching. If I wanted I suppose I could snip a branch off.. but I have never done so.
The sun coral in question is in a tank I treat rather poorly

sad to say.. I don't give it the attention it deserves. and it sometimes gets neglected ie: leaving the light on all night.. it is just a holding tank and I have the sun coral in there because I ran out of room in my nano.
Anyways.. I suppose I could have contributed to the spawning somehow, but I have no idea what did it. I just lifted my black sun coral one day and saw dozens of orange sun corals all over the bottom.. where there were absolutely none before..
I'll try and get that pic tomorrow.