Collection of rent has to do with ownership. That is technically separate from the deed. If the legal description on the deed is correct and the intent was to gift to you, delivery of the signed notarized deed to you or the recorder is sufficient for ownership in you. That said, a correcting deed should be prepared showing the correct APN and address. You should use an attorney for that so you get it right this time.
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While I am licensed to practice in New York and California, I do not actively practice in New York. Regardless, nothing said should be deemed an opinion of law of any state. All readers need to do their own research or pay an attorney for a legal opinion if one is necessary or desired.