(1):

(n.) The assignment of a bastard child to some one as its father; affiliation.

(2):

(n.) One that is derived from a parent or source; an offshoot; as, the filiations are from a common stock.

(3):

(n.) Descent from, or as if from, a parent; relationship like that of a son; as, to determine the filiation of a language.

(4):

(n.) The relationship of a son or child to a parent, esp. to a father.