Disregarding the presence of any parenthetical modifier, adverbs ending in ‘ly’ always modify the word immediately following them. Thus, they do not require a hyphen to indicate which word they modify. This is true in both British and American English. Accordingly, for example, “wholly owned subsidiary,” does not, and should not, employ a hyphen.
wholly owned subsidiary: a subsidiary company that is owned entirely (100%) by its parent company. “Fasty Limited, a company incorporated in England, is a wholly owned subsidiary of Fasty Inc., a company incorporated in the United States.“