[dave in australia]

I'll add a comment about using ez-outs. They are normally used where the head has been abused and the spanner/screw driver has no where to grab, but the thread is not frozen/rusted in. If a stud or bolt breaks because they are frozen/rusted in, 95% of the time, a ez-out will not budge the thread and will then break as well. One thing to think about with ez-outs is that they grip the broken fastener by having a taper, and when you screw them in, they will expand the broken fastener slightly, making the broken fastener even tighter in where it is jammed.
My main method for removing broken fasteners, is to centre pop the broken piece. Then drill a small guide hole carefully remaining central, not hard to do if you go slow. Then drill out the broken piece at a size just under the small diameter of the thread. Then pick out the remaining thread pieces of the fastener, and then clean up the receiving thread with a tap. This negates the need for using a heli-coil.