It really depends on the school and the professor. Is the person you have been in contact with a full tenured professor (superstar in the field or a professor that doesn't really bring in much grant $$)? Does he/she have grant money that can fund you rather than relying on the department to fund you? There are a lot of variables. Sometimes if a professor already has quite a few students, the department might want to give the space ($$ for a student) to a new professor (on a tenured track) so they can get their lab up and running etc. It also really depends on who is on the committee (believe me, sometimes there is animosity between faculty members -- they all think that they "deserve" the space. Also what is the track record of the professor? Have they had a bunch of students before that did not finish or quit (I personally witnessed this before....a faculty member was a jerk and their students quit...needless to say they haven't gotten a new grad student in a l-o-n-g time)? Basically, if the professor can fund you themselves, you get in. But.....every department is different. What field?