What is the mechanism of the uncatalysed epoxide opening with alcohols?
Because of its special chemical struture Ethyelene oxide (EO) is highly reactive material thus easily participate in chemical reactions which includes polymerization. Mechanism of opening of EO's ring in acidic and alkaline medium is given below



If you see in both cases a molecule with alcoholic group ($\ce{-OH}$) is formed.If the epoxyethane is in excess, the reaction can continue and could lead to polymerization. 

A good example is the reaction between EO and water



As explained in wikipedia ethoxylation is an industrial process to make surfactant from EO. Surfactants are chemical molecule which contain both hydrophobic groups (their tails) and hydrophilic groups (their heads).

The end result of reaction with EO and alchol is a long chain molecule with these hydrophobic ($\ce{-R}$) and hydrophilic ($\ce{-OH}$) group