Matt H: It depends. How's that for an answer?

Certain composers tend to stick with who they know. We, for example, handle 90% of Sondheim's stuff and used to handle all of Lloyd Webber's shows before he moved his catalog to Rodgers & Hammerstein. We got WICKED and LOUIE because Stephen Schwartz likes us and we handle 90% of his shows.
Sometimes there's a little wheeling and dealing to get one big title. We got MILLIE because Jeanine Tesori trusts us (and we took VIOLET and CAROLINE, OR CHANGE. MTI also funded a healthy chunk of the Cast Recording for CAROLINE so that we could have reference recordings when the show goes into release). We got RENT because we agreed to take TICK...TICK...BOOM! You get the picture...
Authors who are not currently represented by any of the licensing houses, or those with no scruples and simply are out to make a wad of cash (who could blame them?), are certainly free to bid out their shows to the highest payer. HAIRSPRAY is still up for grabs. The problem with that show is: 1) it's hard to cast so it won't sell as well as something like SEUSSICAL and 2) the authors are asking A LOT of money for the show, so it'd be hard to make the investment back because, well...refer back to #1.
Believe it or not, our boss really wants to pick up GOOD VIBRATIONS because it would sell extremely well. That's why he wants ALL SHOOK UP so badly - it'd sell like hotcakes.
And that's sort of how we obtain properties for licensing...