The fact that a person is injured in another's home does not automatically make the homeowner liable. Instead, the homeowner must be at fault in some way, which usually means negligent, or unreasonably careless. To look at your examples:* Falls down stairs. If this happened because a board was loose, a runner frayed, or a stair rail loose, you would be liable. If it happened when your stair was in good repair but the mother didn't pay attention to the child, who tried to climb the stairs and failed, probably not.* Poison. With a child in the home, yours or another's, the house should be child proofed. Medicines and chemicals should ideally be out of reach; cabinets and draws should be locked if there's anyway a child can get to them. If you took all reasonable precautions, you'd probably not be liable; if you left cleaning chemicals or medicine within reach, you may well be liable however.* Sharp object: see above; you have to child proof adequately.