Wiktionary
avunculate
n. 1 the relationship between a man and his sister's children, generally her sons. 2 (In certain tribal peoples, for example, the Korowai) a special relationship between a man and a maternal uncle, and the mutual responsibilities between them.
Wikipedia
Avunculate
The avunculate, sometimes called avunculism or avuncularism, is a feature of some societies whereby men have a special role in relation to their sisters' children.