what role and contribution do non-specialist and support staff have in
adult nursing care?

Non-specialist, which there are few left in the medical field, support
the primary medical / nursing staff in fulfilling their duties.  I'm
not sure who is considered "non-specialist" anymore because everyone
in medical facilities has some form of training in their area. 
Housekeeping, dietary delivery and transportation assistants all need
basic knowledge of medical problems and have received training patient
information security according to the 1996 HIPAA
www.hhs.gov/ocr/hipaa 

Support staff is also a word for ancillary personal.  Here is a site
that lists definition of support jobs.
www.cranstonarc.org/Employment/def_jobs.htm
  
Here is an article that give salaries for support staff, bit dated but
still standard list. (Near the bottom) Article is how to tell if you
have TOO MUCH staff.  Interesting change.
http://www.mediclicks.net/issues/article05_2.asp


Here is the most complete list I could locate:

http://216.239.57.104/search?q=cache:Z_r9p4clGPkJ:https://salarysurveys.milliman.com/2002HCSjobdescrp.pdf+%22ancillary+staff%22+%2B%22job+descriptions%22+%2Bmedical&hl=en&ie=UTF-8

or the PDF version at:
https://salarysurveys.milliman.com/2002HCSjobdescrp.pdf.

Searches used;
"Medical support staff" +"job descriptions"
"support staff" +medical +"job descriptions"
"Ancillary support staff" +medical +"job descriptions"