The word I recommend is dilate. Merriam-Webster's Collegiate Dictionary, Eleventh Edition (2003) gives two relevant meanings of dilate as a transitive verb:
1: archaic: to describe or set forth at length or in detail 2: to enlarge or expand in bulk or extent
And The American Heritage Dictionary of the English Language, Fourth Edition (2000) offers this intransitive meaning of dilate:
2. To speak or write at great length on a subject; expatiate
There is something a bit odd about these definitions. Evidently, you can say "I must dilate my paper to reach the required ten-page minimum length" without being archaic, but only if you mean dilate in the sense of "to enlarge or expand in bulk or extent." If you mean dilate in the sense of "to describe (or say) or set forth (or write) at (great) length or in detail" without being archaic, you have to speak intransitively: "I must dilate on the subject of my essay, to reach the required ten-page minimum length."