This guy is somewhere on the forums, but I forget where. I pulled this off his cardomain page.
The photo he posted here in explorerforum is after he got the Truxx/Traxda lift, but I'm fairly certain is a photo of his ST with 265-65R18 BFG ATs before the lift.
On my ST, I have 30in 255 Grabber AT2s that rubbed slightly when new.
If you're talking about biggest tire without a lift, stock wheels, no rubbing and you want an aggressive AT, I'd recommend Cooper's ST Maxx or Goodyear Duratracs in 245/75R16, 245/70R17 or 245/75R17 (245/75R17 is the largest of the that bunch).
You might be able do a 255/75R17 or 235/85R16. If you find a friendly tire shop, you could see if they'll let you test a 32in tire (any one will do, 265/75R16, 265/70R17, 235/85R16, 235/80R17) to see if it contacts the top of the fender lining at full compression (of the suspension) (if using a 265 width in testing, test only with the wheels straight). If it doesn't contact, then you'll be fine to run 255/75R17, 235/80R17 or 235/85R16 even in somewhat serious offroad conditions.