ABS = Prevents wheels from locking when braking the car hard
ESP = Is a complete program that keeps sensing the 4 wheels of the car in relation to the steering wheel. If it detects anything wrong then it starts working. It works by braking 1 or more wheels of the car.
ASR = Prevents wheels from spinning for any reason, whether its hard acceleration or due to driving on slippery ground.
If a car has ESP then it should have ABS but the opposite is not true. A car may have only ABS without the others.
So ESP uses ABS & ASR to stabilize the car.
Last thing, many people think that ASR makes the car acceleration worse. This is not true. It is the opposite. If the wheels go spinning then it means that some engine is wasted because its not transferred from the wheels to the ground in order to accelerate the car. The tires spin fast without a lot of noise making the driver think he is getting good acceleration but the opposite is happening. It is just noise.
This is why ASR stops the spinning once it happens by decreasing power & once the spinning stop the power is increased again & so on, so that in the end all the engine power is transferred into real speed on the road.
In short, ASR does not make the car slower. It helps it accelerate better. A very good driver can do without ASR by doing the job of ASR manually by himself. If he detects the wheels will spin he can release the gas pedal slightly, then press on it again & so on. He must be very sensitive but in general the computer doing this job will be more efficient.
Sorry for english. I hope I do not upset anybody :)