For the DIY
plumber, a rusted
presents an interesting challenge for removal. I have replaced a rusted-in garbage disposal
and later a rusted-in faucet
(which, by its leakings, rusted in the original garbage disposal).
Obviously, one does not install a water-handling fixture and simply let it hang in place; it has to be sealed to the sink somehow. In the case of a garbage disposal, the disposal itself hangs from a flange that is sealed against the surface of the sink-bottom with plumber's putty. The putty is not what really what keeps the disposal in place, however - that magic goes on beneath the sink.
The flange is held in place by two triangular pieces of metal with holes large enough to fit around a sink drain in the middle. The flange descends through both triangle-pieces, which are forced apart by means of screw-posts. The triangle pieces are bound to the flange by means of a metal ring which is slipped into place around a ring (and positioning it can be very difficult, as anyone who has ever installed a garbage disposal can attest). Once the triangle pieces are secure, the garbage disposal is mounted to the bottom piece - it screws onto it, if I remember correctly.
The point behind this is to illustrate that garbage disposals, as with other fixtures, are anchored in place by multiple elements. If you have to remove a fixture which has been rusted solid into place, pick the weakest element by which it is secured, and attack that element first. Obviously, the part of the flange that meets the upper surface of the bottom of the sink is many times thinner than the three screw posts that force the two triangle pieces below the sink apart. I was lucky enough to know someone with a saber saw, so I used it to do away with the screw posts, thereby eliminating the need to have someone hold onto the disposal as I mangled the flange, lest it drop and dent the floor beneath the sink. If I didn't have a saber saw, I would have had to have someone hold the disposal, or put a crate under it or something, but I still could have removed the disposal.
The flange remained, and could not be easily removed, since the upper triangle piece was still rusted solidly to it. I took a screwdriver and lodged it under a section of flange, using a hammer to gently tap it further in, then pulled up on it until that section was deformed. I did this all the way around the flange, using a vise-grip to deform the flange further until it could be pulled out of the sink from below.
In the case of removing an old faucet (see my other writeup, installing a faucet), I had the same problem - the fixture to be removed was rusted to a flange on the underside of the sink. It was much more difficult, since it is a lot harder to manouver under a sink than over it, but the same principles worked, and once I figured out that the flange itself had to be defeated - not just the screw holding it in place, the faucet came out with relative ease.