My understanding of the process is that each school submits a ranked list of approx the top 400-500 people they interviewed. The computer system then goes and matches people to the schools--but it is biased to the applicants rankings of the schools.
So, say UT-San Antonio has you as number 248 and UT-Houston as 87 and you don't make the cutoff at UTMB and TCOM. Initially, you will match at UT-Houston since you are in the top 200 (class size). But, as the computer continues through its algorithm, UT-San Antonio is having to go past the first 200 because some of those individuals ranked other schools higher AND they are high enough on that school's list to make the class. At this point, if they go down to #248 (you), you will be put in UT-SA and withdrawn from UT-Houston automatically. However, if they only have to go through 247 people to initially fill their class, then you will remain in UT-Houston's class.
Additionally, all schools that you ranked above the one you matched to will remain active and you may have the option to go to that school if they have to use the waitlist and your number comes up.
Its pretty confusing, but basically it makes you choose your top choices ahead of time instead of after receiving your acceptance(s). The schools will never see your ranking.