My father-in-law and I are very interested in the whole ZDDP thing since he builds engines and has a machine shop. We DON'T want to wipe camshafts on engines we have built - that is expensive! Anyway, we have read a lot about this and spoken to oil company representatives, especially at trade shows like PRI.
ZDDP acts almost like a bearing; bonding to metal and then providing protection against metal to metal contact.
There are a few aspects regarding ZDDP:
1) The amount: Generally, for flat tappet cam engines, you want 1500 to 2000 PPM (Parts Per Million) of ZDDP in your oil. The problem is, I have seen NO oil containers that actually tell you the amount of ZDDP that is in them. Too little ZDDP will cause wear, and too much makes the oil acidic. My preference is to use a good oil designed for flat tappet engines rather than using bottle of ZDDP additive (although I will certainly use additive when I don't have high ZDDP oil available).
2) Fast vs. slow acting ZDDP: Some ZDDP is slow acting, and this is better for continual usage in a broken in, flat tappet cam engine. This ZDDP is slow to bond, but also wears slower. Other ZDDP is fast acting, and this is what you want to break an engine in, since you want that ZDDP to immediately bond and protect the engine.
3) ZDDP vs. Detergents: I have heard that some oil detergents can negate the ZDDP. I personally don't have any information on this, so I can't comment on if that is a real issue or not.
For break in, I recommend Driven break in oil. No, I don't work for Driven or get any kickbacks. But I do have it on good evidence that they have the right combination of ZDDP for break in of flat tappet cam engines. (But note, with high spring pressures above 300#, you should still use weak springs even with the proper break in oil.)