I've used the Easy-out style stud removers and unless they are well and truly seated, they can tend to come loose eat away at the broken stud/zerk etc.
Couple of options. Reverse fluted drill bits are made that will drill when the electric drill is turning in reverse. If you have to drill out a stud to make way for an Easy-out anyway, they are the way to go. In some cases, the drill will even bind to the point where it actually unscrews the broken stud, thus no Easy-Out is required. However, they are special drills and can be hard to find. They also won't work well with a zerk that already has a hole drilled through it.
Second option (which I prefer)
Drill a hole in the offending stud/broken bolt.
Take a 8-12" long drill rod or other high carbon steel rod sized to an appropriate diameter for the stud/zerk that needs to be removed.
Using a bench grinder, grind the drill rod down so you have four flukes with very sharp edges tapering down to perhaps 50% of the original diameter. At the other end of the rod grind two flats for your adjustable wrench. Harden the drill rod with a torch and a container of oil. Once the rod is hardened, drive the tapered end into the broken stud using a ball peen hammer. Keeping hand pressure on the end of the rod use your wrench to unscrew the sud. Sometimes simply hammering in the rod into the stud will loosen it up.
In all cases, use a penetrating fluid first and, if the part can be safely heated without damaging the metal, heating the part can also loosen up broken studs. I've also used insect repellent (bug juice) as a penetrating fluid and it seems to work too, and it also keep the bugs away ;-)
Safety glasses are a must too!
