Looks like you are the proud parent of Phalaenopsis keikis! Keikis is the technical term that you are looking for. Keikis should be left on the parent plant until sufficient roots have formed. Then they can be safely cut off and potted. I'll let the experts around here give you more information. I know what keikis are in general, but don't know the specifics of how to deal with them. I've never been so lucky!
Beautiful phal as well and welcome to the board.