My aunt has POA over my grandmom who is in the last stages of dementia and lives in a nursing home. I want to care for her at my home.

You're in a tough situation if your aunt's Power of Attorney authority gives her control over where your grandmother lives. So, the first thing for you to do is to get in touch with the administrator of the nursing home and find out who they think has legal authority over your grandmother's care, and why. It might be your aunt, acting under the Power of Attorney document. But if the Power of Attorney document only covers your grandmother's finances, as some Power of Attorney documents do, then your aunt might not have the sole authority to decide where your grandmother should live.

Ask the nursing home not only who they consider has the legal authority to make such a decision for your grandmother (assuming that her dementia means that she is legally incapable of making decisions for herself), but also on what legal basis. Even if the Power of Attorney only covers financial decisions, your aunt might have legal authority over your grandmother anyway, as an adult child of your grandmother. But if your grandmother has other adult children -- your mother or father, or other aunts and uncles of yours -- then they might have just as much authority to decide on your grandmother's care. And if they agree with you that your grandmother would be better off at home with you, they might be able to persuade your aunt to agree.

If the nursing home considers that your aunt has legal authority -- either through the Power of Attorney or as an adult child -- and your aunt will not agree to let your grandmother go home with you, then you will not be allowed to take your grandmother out of the nursing home. Legally, the nursing home is not allowed to release your grandmother into your care -- assuming that your grandmother's dementia means that she cannot make her own decisions -- unless the person with legal authority over your grandmother's care has agreed in writing.