remove broken bolts and studs.

When trying to remove a broken stud or bolt, if it is seized in position, easy-outs are NOT the best thongs to use, they tend to spread the bolt against the parent metal and make it harder to extract the bolt. Also if the bolt is say 1/2" in diameter, a 1/4" extractor will not remove it and will tend to break.
The only way to drill out the stud is to go larger in increments until reaching tapping size, then try a tap. If the drilling is not exactly central the threads will be removed on one side requiring a wire insert to reclaim the threads.
If a drill, tap or extractor breaks, the only way to remove it is by spark erosion, see www.sparkeroding.co.uk for more information.
Even with spark eroding the bolt may be totally removed and still need a wire insert.