"drop off" is correct and usable in written English. You can use it to refer to the act of taking somebody or something somewhere and then leaving it there. For example: "I'm going to pick up my daughter from school and then drop her off at home.".
I'll drop off the money.
"They don't drop off".
Drop off laundry.
(Translation: drop off dirty dishes here).
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MA of Applied Linguistic, Maquarie University, Australia