It sounds like you are talking about Cost Per Acquisition offers - commonly known as CPA. There are lots of CPA affiliate networks (scan the threads and you'll see news and reviews about many of the top ones). As for the best, they each have their own areas of specialization (many are generalists) and payouts vary depending on what type you are looking for. What type of offers are you specifically looking for or what does your site focus on ?
I'm not really sure what the actual name is, here's an example of a page **This is not mine just an example** offers.sleepdisorderconnect.com/?vendor_hash=d4dad3924551499c9f16ce8a5c50681d49aeec3e02e94&provider_code=DTK&affiliate_id=CD1030&keyword= **This is not mine just an example**