Someone who converts as a minor (younger than 12 for a girl and 13 for a boy) is required to fulfill the requirements of conversion, that is circumcision and mikvah, but are not required to perform an 'acceptance of the mitzvoth'. The conversion instead is done al daat beth din, the acceptance is done by the Beth Din presiding over the conversion. The child lives as a Jew until their bar/bat mitzvah and they then have the option of rejecting their conversion.