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Let's see if this works -
http://www.familysearch.org/Eng/search/frameset_search.asp?PAGE=ancestorsearchresults.asp
If not go to www.familysearch.org and type the name in the surname box, and specify England.
Judging from a websearch Asselbrough seems to be the earlier, and Durham spelling. Hazelbrough appears as the name is dispersed. It has got to be a place name but I can't identify one, though there is a Hazelborough Wood in Northamptonshire. Assel- may be from the Old Scandinavian male name, Askell; that's the origin of Assel- in the East Yorkshire place name Asselby.
This is a very rare surname, which always adds to the difficulty in obtaining information.