"drop off with" is correct and usable in written English.
You can use it to describe someone leaving something with someone else, or to describe the transfer of an object from one person to another. For example: "Please drop off the package with my neighbor when you're done."
The fact that they drop off with each cell division is thought to protect us from cancer, when a cell is hijacked and proliferates continually.
However, take August figures with a pinch of salt because activity tends to drop off with large swathes of the country on their summer holidays.
Low pressure on Tuesday and Wednesday will move away to the East, and chill north-westerly winds will cause temperatures to drop off, with wintry showers on both days.
Now another group of scientists have published research that pushes back, revealing the new neurons are produced in this brain region in human adults and does not drop off with age.
Since the New Year they have been leaving at the rate of almost 2,000 a day, dismaying politicians in East and West who had hoped that the frenzied flight of last fall would drop off with the promise of free travel and free elections.
In the Rugby Championship, Argentina used to drop off with 15 minutes to go.
He was dropped off, with no luggage, at Sangatte's barbed-wire gates in a Mercedes.
Watford's form has dropped off, with two wins from the past 11 league matches.
Also, since light drops off with depth, not all life within the lake is receiving the same amount of energy.
One moment, we're watching Frankie being dropped off with Cindy's father (John Doman) for a sleepover.
Interestingly, one sensor can pick up information from anywhere in the brain, but the strength of the signals it measures drops off with the square of the distance.
