Dear Cortilla...
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I try to suit my answers on Pprune to the geographical area and background of the people who ask questions, such as you with FAA and UK... so, like you I am confused as well. You "are a little left of me" and I dont know your activity or background to answer you better.
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In the USA there is a dispatcher certificate (licence) and the privileges and duties vary depending the type of air carrier operations, such as domestic, flag, supplemental or commercial operators. Essentially, dispatch release may or may not be required for USA operators (the other form of dispatch ground operations is called "flight following").
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Generally, a USA air carrier will have a few licenced dispātchers, and a few assistants to issue and forward documents to the operating flight by SITA, fax or email. but a dispatch operations office have many assistants who are not "licenced" but work under supervision and responsibility of dispatchers. Some just "forward papers" as you well say.
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Realize also that a FAA dispatcher has passed a written and practical exam, that is equivalent to the test for the FAA/ATPL, so essentially, except for actually flying an airplane, a dispatcher has equal knowledge to a captain as far as meteorology, navigation, regulations, aircraft limitations and flight planning.
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Then, know that there is big regulatory differences between a dispatch organization and flight following, although in practice, the two are very similar in their activities, and handling of documents.
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I dont know the legal differences with the UK air carriers, but in practice, I believe their duties and responsibilities are quite similar. I work in Argentina, where we essentially follow US/FAA airline standards and regulations. When I show-up 90 minutes before a flight to my operations office, all the flight documentation is ready for us, from flight plans, oceanic tracks, payload info, fuel requirements, weather reports and forecasts, NOTAMs and maintenance status of the airplane. Off base, i.e. in Europe, the handling airline provides us with tons of papers and documents forwarded by our Buenos Aires ops office. During flight, we remain in contact by SATphone or HF phone patch with that office for any updates.
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Any questions?
Happy contrails