On the blades I zero grind, I take them to about .010 for carbon steel and .005 for stainless, before HT. After HT, I grind to near sharp....carefully avoiding heat....and then switch to flat stones or diamond plates to finish the edge.
Most zero grinds are actually slightly convex ground at the edge. It is very hard not to round into the edge.
That said, there are very few blades that do better with a zero grind than they would with a small secondary bevel. Sashimi blades and microtome blades are OK as true zero grinds. Most all others should have a stroke or two done at about 15 degrees or higher to strengthen the edge.
Just to illustrate how small the edge angle is, a zero ground knife with a 1/8" spine and 1" tall bevel will have a 7 degree edge. That is very thin. Any abuse, even a minor bump, and it will chip instantly. Cut any hard materials and it will dull quickly.