The early distribution of these three surnames provide us with some good clues concerning their points of origin
You can compare these with maps of their nineteenth century distributions here.
Anstis is from a medieval first name.
The origin of Argall is unclear but the map below suggests that the place Argal (near Falmouth) may not be the source.
Arnall is a spelling of Arnold.
Cornish studies resources 
Hi,
I have started Researching my Family Tree with my mum’s side, and have got as far as John Rule who was born 1600 in the Parish of Camborne, Cornwall, and died in the Parish of Breage, Cornwall in 1680/81.
I have drawn a blank after this due to there not being very much information on who John’s Father and Mother were. I was going to leave it there but found your web site and thought it might be interesting to see where the name Rule came from, it appears that there were the more affluent Rule Families in Camborne and then the less affluent Rule Families further down towards St Hilary, Marazion and Breage, which is where most of my ancestors hail from. There is some confusion from different sources as to whether John Rule married into the Rolle family, as yet there is no evidence of this marriage taking place so I have discounted this until I have more solid information. I have no way of knowing who John’s Mother and Father were but thought I would ask if the Rule name originated in Cornwall, it might help my research further back.
Hope you can help.
Kind Regards
Susan
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The distribution of the surname Rule in 1881 suggests two possible separate points of origin, one in Cornwall and the other to the east and south of London. It’s actually a bit of a puzzle, but was present early in Cornwall as Rewell or Reyll.
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