How to write and abbreviate a "scientific name", under the Linnaean system, and according to the International Code of Zoological Nomenclature.
The species is Tyrannosaurus rex, where rex is the specific epitetus. Here is called species because it gives the species, but it does not designate a species itself (it is never written just rex whithout the genus).
*Complete species should include author and year, though.
Example extracted from "The Complete Dinosaur, Second Edition".
Additional info (avalaible in Wikipedia):
T. rex may also refer to:
Tachyoryctes rex, the king mole rat, a rodent species Tetragonodon rex, a seed shrimp species native to the Mozambique Channel Thoristella rex, a sea snail species endemic to New Zealand Trialeurodes rex, a whitefly species Tyrannasorus rex, a fossil beetle species from the Miocene Tyrannobdella rex, a leech species Tyrannoberingius rex, a fossil gastropod from Miocene Alaska
Sort of thing I know deep down already yet always write the wrong way - especially for "T. rex" (probably the first time I've ever written it correctly!)
Extracted literally from "The Complete Dinosaur". According with Holtz, there is a debate about whether to use the trivial nomen of the wild ancestor for domesticates or not.