Not a huge amount of paperwork on our end. We have to fill in an MOR which takes about 20 minutes. It's a massive annoyance though and then has to be investigated at our side through the investigation team. Not sure how long it takes them but it involves them pulling the radar tapes and RT to look at what happened.
At the time it can cause our hearts to skip a beat as we try and work out what just happened when we're working normally and suddenly get a told by an aircraft that they have a TCAS RA.