Does signing that you are a contact person OR next of kin for a nursing home patient place any financial responsibility on you? Does it place any other legal obligations on you? Can you assist a person being admitted to a nursing home without taking on any legal responsibility?
By assisting, help them find one, get them there, go into the Admissions office with them, provide information that is required, and possibly provide your info as a contact person. Given that nursing homes can boot patients (dangerous would be one reason why) are you potentially the one who has to clean up the problem? (Come collect them, possibly find them some place to go, etc.) or would the supposed system work with the social workers of the nursing home or senior services system getting them placed appropriately?
The answer to the first two questions are no and no, unless otherwise specified in the document you sign your name to. The last question is a little fuzzy. What do you mean by assist being admitted? If you drive them to the home and get them there safely you have no further responsibility. If you're talking about more than that then you have to tell us.