<p>These things are cyclical. At times, fresh blood is desired, ant others there is a real attempt to keep one’s own talent. It depends on the faculty consensus. Quality at the grad level has more to do with who one studies with and what the program is rather than the name of the school. For example, it’s hard to beat UC San Francisco in the neurosciences. </p>
<p>Relationships with other recommending professors has a great deal to do with who is admitted where. More folks know and respect more folks from more places, as marite implied. Though faculty tend know one another from the same institution, top students from anywhere have a good chance of being admitted to top programs if their profs are known and respected by peers. As the number of faculty jobs are not increasing all that fast (until the boomers retire at least) many graduates of top programs are teaching in 3rd tier schools and are recommending students. As I have mentioned before, a friend has never failed to place his 3rd or perhaps 4th tier students in top Ph.D. programs often ahead of others from elite undergrad schools.</p>