Is the esse that perfected the humanity of the Word, common to all three Persons of the Blessed Trinity or to Only the Word?

Is the *esse* that perfected the humanity of the Word, common to all three Persons of the Blessed Trinity or to only the Word? I ask because the divine *esse* is identical to the divine nature. And the term "divine nature" could be understood in two senses. In one sense, it refers to all three Persons of the Blessed Trinity. In another sense, it refers to a particular Person of the Blessed Trinity, which is in this case the Word. Or is it the case that it's both depending on which sense is used?