I believe each school/department has some allocated spots that they can give to students. For those allocated spots I don't think one even needs to apply. This is the letter I received a while ago:
Dear Incoming Dental Student,
You have been selected to receive an allocated
position in our university-owned apartments. The
newest apartment complex, Weyburn Terrace, is
available for single graduate students and is
located within walking distance to campus. We also
have positions for family housing in the off-campus
complexes located in the Palms/Mar Vista area (a
limited number of single students may choose to live
in this area as well).
In order to receive a position, you must respond
back to this email by [DAY], [DATE] at [TIME].
If you are not interested in graduate housing,
please let me know so that others can receive
consideration.
Please indicate if you would like single student or
family housing in your email response. Single
students must choose between Weyburn and an
off-campus complex. Your choice must also be
reflected in your graduate housing application.
Remember to visit the housing office website at
www.housing.ucla.edu/myhousing to submit your
application and non-refundable $30 fee if you
haven't already done so. Note: submitting the
online application is a critical step in order to
receive one of these positions.
Feel free to contact me at [xxx-xxx-xxxx] if you have
any questions.
We hope you take advantage of this opportunity.