Actually, the single adverb anymore is standard AE (confirmed by such sources as Bryan Garner and the American Heritage dictionary). It's typically used in negative sentences, it refers to time, and it's equivalent to "any longer" or "still":
I don't have those cherries anymore. (I had them earlier; I don't have them now.) She doesn't live there anymore. (She did live there; she doesn't live there now.)
The two-word phrase any more, also typically used in negatives, refers to quantity:
I don't want any more tea, thank you. (I've had enough.) I don't have any more cherries. (I had a quantity of them, but they're all gone.)
P.S.: Another, limited use of the single word anymore, which is heard in some parts of the US Midwest, is not standard and is considered dialect. It's used to mean "nowadays" (as in "prices are high anymore"). That's the usage Kate mentioned in post #62 in her "don't see him around" example.