Wifi is off when phone is turned off. After phone is turned back on wifi turns itself on. Smart network switch is off, Network notification is off. Once I remember to turn it off it stays off. Same thing happens to my wifes S III. Thought it might be related to a new router, but wifi turns itself on with router turned off. I haven't downloaded any new apps for awhile and wouldn't know howto tell if any were causing a problem.