I've run into a situation that I've not been able to find an answer for. If a corp rezzes an ice with Oversight AI, and the runner derezzes with Emergency Shutdown I know the hosted condition stays. But what happens if the corp then uses Bioroid Efficiency Research to rerez that ice? Does the BER condition overwrite the OAI condition? If not, how are the conflicting conditions resolved?

I would imagine they both trigger. The corp will choose the order of resolution, but as one of those effects is to trash the ICE it won't really matter.

Both BER and OAI apply. Since both effects would occur simultaneously, the corp gets to decide the order in which they resolve. So you can either derez the ice for BER and then trash it for OAI, or trash it for OAI straight away, preventing the derez from BER. Either way, your ice will get trashed.

Ok, makes sense. Thanks for the response.