Hello Rovi, "To hand" and "at hand" tend to be used of objects, and mean "easily accessible". "On hand" tends to be used of people, and means "waiting and ready to act". Best wishes, MrP
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CalifJimAmerican English must be different. on hand is definitely for objects, particularly ingredients.
My wife wanted to make a cake, but she didn't have any [flour / eggs] on hand.
to hand sounds completely British. I don't ever use it. I'm not sure I ever use at hand either, except maybe as an occasional substitute for