When Turkish people speak to children, they often address them with the kinship term that the child is supposed to use for the speaker. For example a mother may call her child "anneciğim" ("my dear mother").
I've been told that something similar exists in Arabic, Italian, Greek, and Russian, at least for the word "mother" (in Turkish it works with many kinship terms). But, to my knowledge, it doesn't exist in English or French for example.
Is there a name for this phenomenon? How common is it? Is it confined to a geographical region? In short, how can I find more information about it?