In proper conditions, H2SO4 reacts with C2H5OH:
H2SO4 + C2H5OH = H2O + C2H5OSO3H
and the product, as you see, is alkyl sulfate. It can even be isolated from other substances, as far as I know. But it's an unstable substance, and it easily reacts with C2H5OH:
C2H5OSO3H + C2H5OH = (C2H5)2O + H2SO4
I think, if you increase the amount of H2SO4, it would actually lead to the production of akile sulfates in both reactions, and you would get more alkyl sulfate this way.