In my conversations with several PhD students/PhD graduates/professors, I hear repeatedly that he/she got in through a direct recommendation from his/her professor to a professor at the target school, he/she had a direct discussion with his/her intended advisor at the target school through someone who connected them, or each person who got in to the program has some sort of ties to some faculty member in the school. My serious question is - do people who don't have such connections get in? Are some schools known to be more about such connections? Also, for people who don't have such connections, what can they do to up the chance to getting themselves on the radar screen (assuming the person is a strong candidate) to the relevant faculty members?
Thanks!