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After the repeal of the Immigration (European Economic Area) Regulations 2016, EU citizens will enter the UK as any other non-UK citizen under the Immigration Rules. They will be subject to the same questions and grounds for refusal as other foreigners, and the government's recordkeeping will be the same.
There may be some exceptions for EU citizens who are participating in the "settled status" scheme, but that will not apply to people arriving after the UK withdraws from EU free movement.