All three were written in response to a Challenge/Prompt Fest of some sort.
All three mention members/descendants of the Black family.
All three include Harry at some point of his life: adult, baby, schoolboy.
All three involve the relationships of parents with their children.
All three emphasize the value of family and/or friends.
All three involve godfathers: Harry/Teddy, Sirius/Harry, Snape/Draco.