Sorry, is it Hold onto OR ON this cup for me while I tie my shoes

Hold out means to continue, remain, stand your ground. For example: The soldiers will continue to hold out until ordered. Hold off means to refrain from doing something. For example: Hold off on finishing up those repairs until I have enough to pay you. Hold on can mean the same as hold out but is more commonly used to describe keeping a grip on something. For example: Hold onto this cup for me while I tie my shoes.