father, daddy
爹 centers on a father figure, specifically a familiar or affectionate term like 'dad' or 'daddy'.
爹 combines 父 (father) with 多, which likely contributes a phonetic element. The exact historical development is uncertain, but the character is used in Chinese as a term for father.
A father (父) with many (多) children is a dad: 爹.
For タ, imagine a dad saying 'ta!' as he hands something to his child: ta -> タ.
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