on someone's hands

on (one's) hands

Imposed upon one, especially as one's responsibility to confront or manage. I'd come and pick you up, but I've got Jane's kids on my hands this weekend. If the two countries don't stop this antagonistic back-and-forth, we could have a nuclear war on our hands!
See also: hand, on

on (or off) someone's hands

having (or not having) to be dealt with or looked after by the person specified.
See also: hand, on