The most logical effect for a center tear is Ashes on the Arms. Richard Osterlind has a great handling of this on his Mind Mysteries Too DVD set.
I personally prefer to use an I*p P*d, as it makes the effect much more clean and direct as I never touch or go near the paper they have written on. Also, there is no pre-folding, line drawing, or any other specified way of writing the name down or folding up the paper. The whole thing is casual and nonchalant, and allows for a great convincing line as to why having the name is even being written down. Handing them the pad I just say, "Here, write down the name you're thinking of... Good, now tear it off and put it in your pocket. That's just so you can't change your mind, and in case I'm wrong you can prove I'm wrong later" (B. Smith). This makes the whole writing down of the name incidental in the effect as opposed to the focus point.
That said, I do sometimes use a center tear. When I do, I tell them I want them to "make that name real now. Turn that name into a real memory." After they write down the name and fold the paper up, with my head still turned away, I ask, "Have you done that?" as I reach out for the paper. When they hand it to me, I keep looking away and ask if they can see through the paper as I display it. After they say "No," I continue, "Well let's just be sure"--and I do the first tear. "Now that you've done that (referencing them writing down the name) we don't need it anymore." I then ask them to hold the pieces in their fist and I turn their hand palm down. I ask them to visualize the name on the back of their hand, and using some suggestion, cause them to see the letters (Benjamin Earl has some good work on this on his Skin DVD, and of course Luke Jermay's works). I then continue, slowly revealing the name as I read the letters they're seeing off the back of their hand. Asking them to point to the first letter they see is a good starting point for this, then continuing from there.
Hope that added some value to the conversation.