Water extraction of ethanol from petrol
Water and ethanol are highly "miscible"; a science term that means virtually any amount of water is fully soluble in ethanol, and vice-versa.  The next thing to consider is that ethanol and gasoline are quite miscible. Think of E-10 (10% ethanol) all the way to the E-85 some petrol engines are designed to function well on (with  some loss in power output).
However, water is very poorly soluble in pure gasoline.
So adding when water to E-10 the water mixes well with the ethanol, but the H2O/ethanol mix looses solubility rapidly as more water is added.
In theory, if you set up a separation flask, basically a clear glass vessel with a petcock at the very bottom, filled it at room temp with a gallon of E-10 and added ~3 tablespoons of water, shook it all up then let it settle to separate, you could drain away the bottom (denser) layer of liquid, which would be the water/ethanol mix, an leave you with ~0.9 gallons of relatively alcohol-free petrol. 
My final remark would be to ask why anyone would wish to do this as I can think of no reason in the world why someone would bother.