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dominate [dominated, dominating, dominates]▼(to govern, rule or control by superior authority or power)
verb
[UK: ˈdɒ.mɪ.neɪt] [US: ˈdɑː.mə.ˌnet]

hold sway▼(to have the greatest influence (over someone or something), see also: dominate)
verb

prevail [prevailed, prevailing, prevails]▼(To be current, widespread or predominant; to have currency or prevalence)
verb
[UK: prɪ.ˈveɪl] [US: prɪ.ˈveɪl]