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The Bac (purple) smooths out your idle under normal conditions. Typically once the mechanical settings for the engine idle are set, the computer uses this to try to keep the engine running in a steady idle state.
The AWS (green) is used when you start your car to raise the idle to get your engine warmed up quicker. As most folks on here would agree, you don't want to be goofing around and break a seal because it was cold.
The ABV (on back of intake) is used for transient loads. When you are at idle and the computer is using the BAC for idle control, this little guy adds extra air to the mix when transient loads like power steering or A/C kick on. It just helps keep your engine from bogging.
If you are going super drifto on your car, you can remove these. If not, I'd leave them hooked up. I put these back on my car (pain in the rear getting the full set) because I like the creature comforts in my car and was tired of having to flog the gas whenever I was puttering in traffic. New vacuum hoses are a must though. I got a silicone hose kit and replaced all of them.