How are antibodies transmitted from the mother to the child during pregnancy?

Same as everything: Baby only grows because it gains nutrients & oxygen from your blood through the umbilical cord/placenta. In the same way, your body shares an amount of antibodies actually more by weight than you retain for yourself. They move in & out of baby the same way nutrients move in & wastes come out. Your body gets rid of waste & returns antibodies/nutrients. When the cord id clamped the transfer stops.