Skypilot, I agree, the controversy within climate science is all about the climate sensitivity (but you wouldn't think that around here - here its about whether its a scam or not).
"...in effect temperature rise will never be exponential but will quickly taper off as the atmosphere becomes saturated with co2" - agreed. We would probably struggle to get to 1200 ppm even at the rate we are going, having said that, if one could imagine 'excessive' feedback loops (melting clathrates, high level CO2 expiration from the oceans, constant bush-fires, no more permafrost) then I guess we could get there, but theoretically there is no saturation point that I am aware of, I guess it is a practical limit, assuming we still have enough plants producing oxygen that is.
The saturation point I have seen argued about is the point where adding extra CO2 makes no difference to temperature, but I'm not sure that point exists, is that what you are referring to?
Re: the various estimates for temperature rise - these different estimates are usually based on different scenarios e.g. business as usual scenarios versus rapid action scenarios. The IPCC and the IEA both do them and possibly others.
I don't agree the models are "totally useless" at calculating the climate sensitivity and feedbacks. They are getting more sophisticated all the time and from what I have read they are remarkably accurate these days. Obviously you can test them to some degree by kicking them off and comparing actual weather/climate results against what the running model says.
