I'm hoping you will still receive this message as your posting was 8 Feb 2000. I have just added the BOXILL name to my BOXALL (and Variants) One Name Study. From the information that I have gathered so far it appears the BOXILL variant may strictly be from Barbados. My thoughts on what I have gathered todate indicate to me that the name may have begun as BOXWELL changing to BOXWILL and then BOXILL or BOXHILL which are predominante in Barbados and the USA. I would love to here details about your BOXILL family and see if you have a connection to Barbados.
You can reach me at BOXALL@one-name.org