I am just posting the comment as an answer. One reference is EGA $\textrm{IV}_2$, Section 6.11, pp. 158-163.
Edit. Hans points out that in EGA only the absolute version of the results are proved, whereas he is asking about the relative version. However, the same proofs as in that section prove the relative result as well, almost verbatim. Here is a link to an extract of a preprint of Chenyang Xu and I where the details are made explicit, http://www.math.stonybrook.edu/~jstarr/papers/RSCff_02_23_13a.pdf