Bill Cosby -- Alma Mater Runs for the Hills ... Amid Testimony of 'Enquirer' Trade-Off

One of Bill Cosby's alma maters cut all ties with him on the same day it was revealed that Cosby struck a 2005 deal with the National Enquirer to stop it from publishing a rape accuser's story.

The University of Massachusetts Amherst -- where Cosby received his masters and doctorate in education -- announced Cosby agreed to step down Wednesday as co-chairman of the school's fundraising campaign. A UMass rep said he now has zero connection with the university.

Late Wednesday ... previously sealed court docs were released from Cosby's molestation case involving a staffer at his other alma mater, Temple University. The docs include Cosby's sworn deposition, during which he said he agreed to give the National Enquirer an exclusive interview -- and in exchange it killed a story about a rape accuser named Beth Ferrier.

In the depo, Cosby said he was afraid Ferrier's story would bolster the extremely similar accusations being made by the Temple staffer, Andrea Constand.