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to become attached (to); to take (to); to become affectionate (with); to be tamed; to get close (e.g. to someone emotionally); to become intimate (with)
近所の猫が最近私になついてきた。
A neighborhood cat has recently become attached to me.
人見知りの子どもがすぐになついてくれた。
The shy child quickly warmed up to me.
保護した犬が新しい飼い主になつくまで時間がかかった。
It took time for the rescued dog to bond with its new owner.