Generally, if a person is allegedly incapacitated(aip), for others to take care of the aip's person and financial matters, a guardianship under mental hygiene law article 81 will have to be commenced by the filing of a petition, testimony will have to be taken, a doctor attesting to the incapacity will have to provide his or her opinion, and if incapacity is found, the court will issue an order and judgment appointing the petitioner. The process can take several months and is somewhat complex. Out-of-state relatives can petition to be the guardian(s), and will have to appear in court for the hearing, and thereafter, in carrying out their duties.
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If a person cannot understand the consequences of their actions, then he could not sign a power of attorney or advanced health care directive. So, if you needed to make decisions for this incapacitated person, then your only option would be a guardianship (called a conservatorship in certain states).
I cannot speak to NY law, but in NJ, a guardianship would work roughly as follows: you, the proposed guardian, would retain legal counsel (you could do it yourself but that would be unwise). the lawyer would draft the complaint and other papers. Two doctors would need to example the incapacitated person (soon to be the Ward) and would render an opinion that he could not handle his affairs.
that paperwork would be filed with the court and a court-appointed lawyer would be appointed for the Ward. the court appointed lawyer would advocate for the Ward's wishes and report to the court as to whether or not you should be the guardian.
In some counties in NJ, if everyone agrees that the Ward needs a guardian and you should be the guardian, you don't even have to go to court. In some counties you have to go to court but it's a rather pro forma event that lasts about 5 minutes (assuming you are the only case in the courtroom, which is unlikely, so you'll wait your turn).
once your appointed, you have to file accountings of the wards assets, income, and liabilities every year.
this all assumes that the guardianship is uncontested meaning no one questions your application to be the guardian. if the ward doesn't want a guardian or your as a guardian or another family member objects, it becomes litigation that could drag on for a long time.
In NJ, if you were the closest relative, it wouldn't matter if you lived in another state. can't say that is the case in NY.