Legal Question in Real Estate Law in New York

Interesting question.

My first thought is that while you have described this transaction as a gift, it doesn't qualify as a gift because your relative does not have complete control over the property. This would be called an "incomplete gift" until such time as it is exclusively in your relative's name, and only then would it be a complete gift, and you would have no recourse.

Until then, either party can terminate a joint tenancy and take the entirety of the property for themselves. I would get that done before your relative wises up and removes your name and keeps the entire property and there would be nothing you could do about it.