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What application form are you referring to and what is nationality of the person travelling with them?
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Ok. Anyone travelling with your children must have leave to enter the UK. If the person you are proposing to travel with your children is Nigerian, she will need to have a visa. Also you may need to speak to the airline regarding their policy in this situation. I am certain consent from both parents will also be required. I expect there to be a strict policy regarding children travelling without their parents or family members especially if they are very young.
The person travelling will need a separate visa to travel.
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