The relationship between England and the 13 American colonies can be described as

Host country (England) and colony (13 American colonies).

Explanation:

There is a lot of different relationships that you can use to describe England and her 13 colonies, and the choices may well depend. However, in the broad scheme of things, the 13 American colonies are, well, colonies, or areas that Englishmen have settled and that created communities that, when successful, slowly grew in size to become what was later known as the 13 colonies. Therefore, England was the motherland, and the American colonies were colonies.

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