Originally Posted by united.com

Getting to the gate
Standard strollers, folding wagons, and car seats can be used to get to your gate and then checked for free. They’ll be returned to you on arrival. Collapsible strollers can be stored in-cabin. Car seats can be used onboard your flight too.

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You can check one car seat and one stroller or folding wagon per child you’re traveling with, for free. This can be done at the gate or ticket counter. Large or non-collapsible strollers, and non-folding wagons must be checked at the ticket counter. However, they’re also free.