Stone-Čech remainders of nowhere locally compact spaces

The remainder of a compactification αX of a space X is the space αX - X. For a nowhere locally compact X, it is shown that if αX - X is extremally disconnected, then αX = βX. Conditions on X are obtained which characterize when βX - X is extremally disconnected. Also, conditions are provided which characterize when βX - X is zero-dimensional.