Unsurprisingly, this trope is initially parodied in Chapter 43.
It's played much, much straighter, however, with Hilda's Heroic Sacrifice.
Hilda:"The Master is now in your care. You're the only father he has in this world..."
And again in Chapter 141, as Hilda cries over how Oga keeps on insisting that she needs to get her memories back and refusing to accept her as she is.
Hilda:"Am I really that unwanted?"
En's breakdown at the end of the Akumano arc. While the scene is mostly Played for Laughs, it's still hard not to feel sorry for the little guy, especially if you've been abandoned before.