On contacting faculty and asking if they're taking on advisees to help your chances of getting in -- sorry to say, this has a low likelihood of working (to the person above who said it did work, my guess is that your clear research statement had more to do with your success). All schools have a small subset of faculty who make the admissions decisions (usually about 4-5 faculty members), and the admissions committee is rotated every year (and you won't know who's on the committee). Since admissions committees have read all the applications and thus can make all the relevant comparisons among the files, they usually don't take into consideration a single faculty member's suggestion that they admit someone with whom he/she had a few interesting email conversations. I know everyone wants to believe they have more control over this process than they do. But it's better to know now that your best shot is to have a combination of good grades, good gre scores, research experience, and a fantastic research statement.