Q: A neighbor asked to leave a small desk in my driveway for the day. It suddenly began raining, and the desk got ruined in the rain. Am I responsible for the desk?
A: A guardian only becomes responsible for an item if he accepts responsibility for it. This does not require any formal declaration, though, and it suffices to say, "Leave it with me," or "I'll take care of it." However, simply saying, "Put it down," is not necessarily understood as accepting responsibility, unless circumstances clearly indicate so, e.g. if the owner is going far away (C.M. 291:2; SM"A 291:5).
Similarly, allowing a neighbor to place an item in your yard or driveway does not indicate acceptance of responsibility for it, unless your language indicates so. Some say, however, that giving permission to leave something in your house is considered as accepting responsibility for it (291:3; Shach 291:8-9).
Therefore, if you allowed the neighbor to leave the desk in the driveway, but did not indicate that you accept responsibility for it, you are not responsible. [You should have made an effort to protect the desk from the rain, however, as a form of hashavas aveidah (259:9).]