Broadcast across American university (8)
I believe the answer is:
transmit
'broadcast' is the definition.
(I know that broadcast can be written as transmit)
'across american university' is the wordplay.
'across' becomes 'trans' (prefix meaning across or over).
'american university' becomes 'MIT' (Massachusetts Institute of Technology).
'trans'+'mit'='TRANSMIT'
(Other definitions for transmit that I've seen before include "Communicate (an idea)" , "Send from one person to another, or broadcast" , "Broadcast (a signal)" , "F. name; Hamlet (anag.)" , "Pass on (message)" .)