Way out in left field.
Beside (to the side of) = à côté de,
côté being pronounced ko-tay. (Bilingual Canadian here!)
A de cote would mean something like "has rib" or "has dimension". If it meant anything, which it really doesn't.
I've been doing YDNA analyses of both sides of my family. After discovering that my gr-grfather was really born a Hill, I thought my job was done. Turns out that genetically he is a Hore, or Hoar, or Hoare. What is the origin of that name? Wise grey-bearded elder, from the dictionary definition of "hoar" (e.g. hoar frost)? That's a prevailing theory and I think it's silly, since there are separate and unrelated Hore/Hoar/Hoare families. How about: they were mining folk in Cornwall, so they're named for the copper oar (which is how the name is pronounced)? On my other side, feeling secure in my trail of parish records back to the 1500s, I've just discovered that my best genetic matches are with a family called Weedon, a name that appears nowhere in my tree or in the vicinity of my ancestors' stomping grounds. Were they weedy-looking people? I guess it comes from the name of the place in Buckinghamshire. Where did
it get its name? Ah ... from the Anglo-Saxon words for temple and hill. Haha, and I thought the Hill was on the other side of my family!
I don't place much store in potted name stories produced by scroll-selling outfits, but this one looks reasonable to me, given that we are actually talking about Devon/Cornwall in your family's case.
http://www.surnamedb.com/Surname/AddicoteRecorded in a number of spellings including Addicott, Addicote, Addeycott, Edicot, Adiscot, and Adacot, this is an English locational surname, from the village of Addiscott, in the county of Devon. The village name is of Olde English pre 7th century origins and derives it is said from 'Aeddi', a male personal name of that period, plus 'cott', a house with about four acres of land, enough to raise a family upon. An alternative suggestion is that the village name is descriptive and means 'at the cott', which is also quite a logical explanation. ...So ... Eddie's Farmhouse.
I would settle on that one if I were you! And that will be what the Lordship of Addiscote you can buy cheap relates to, I imagine. The sale details specify that it is in the parish of South Tawton, and Addiscott shows on the map here:
http://www.streetmap.co.uk/place/Addiscott_in_Devon_377611_04611.htmAddiscott Estate, Addiscott Farm, and Addiscott Home Farm, right by Addiscott Cross that you mentioned earlier, just west of Okehampton. Perhaps the family took the place name with them when they branched out from that location.