One SLIGHT problem: The very same reason that trap & kill fails is the very same reason that TNR fails. You just cannot trap them faster than they breed, are dumped by criminally irresponsible pet-owners, or as fast as they out-adapt to any trapping method ever invented by man. ANY method dependent on trapping is doomed to fail before you even start. But hunted-to-extinction most certainly works. It even worked on something as small and prolific as The Rocky Mountain Locust that used to darken they skies of half of N. America at one time. A simple 50-cent per bushel bounty on them made them no-more, forever, extinct, in only a few years. It'll work even better and far faster on something that breeds even slower and is easier to target -- like cats.

It worked where I live! I've not see even ONE cat for miles around in over EIGHT years now.