or, to hand,
also, at hand
- present, nearby, close, or easily accessible
- ready to help
- immediately available
- ready to be used if needed
- in stock
- My parents are always on hand if we need a babysitter.
- There is medical staff on hand 24 hours a day in case of any emergency.
- Being the mother of young children, she always has wet wipes on hand in her bag.
- I always keep some paracetamol on hand in case I get a headache.
- It’s always good to keep a bit of cash on hand for car park meters or a tip in a restaurant.
- The computer shop will have experts on hand to help you choose the right laptop for your needs.
- The accounts department always has some petty cash at hand for birthday cards and the odd bunch of flowers when someone is ill.
- I’m afraid I haven’t got my diary to hand. (in the sense of near or close.)
There was no history available for this phrase, but it seems pretty literal, and all three prepositions (on, at, and to) have the same meaning. For most of us, our hands are attached to us, so if something is within the distance of your hands, then it is on, to, or at hand.