My split tails are smaller diameter than the climbing rope 8 to 10 mmm works for me. On the other hand I also have some S-tails I made with Blaze and they work fine also like Moss mentioned. So your preference is the key here.
The smaller the diameter of the split tails rope, the more it grabs on your main climbing line, but do not get them too small because it is a risky situation. ( I would not use something like 6 mm rope to make a split tail.)
The Split tails that Sherrills sells are (mostly) smaller diameter than the main climbing line. (Check with them for suggestions)