What are my model rights about paid photos?

Just because you've paid doesn't mean some automatic rules come into force. As mentioned in the comments above, it depends on the specific agreement between you and the photographer. So, what did you agree with them?

If this is a real situation and not just hypothetical, and the photographer is arguing that you don't have legal right to use the photos as you wish, the simplest and cheapest solution might be just to walk away and have your photos re-taken by another photographer, with a satisfactory agreement in place beforehand this time.

Edit to add: Personally, it does seem unusual to me that the photographer would insist their watermark be kept on photos that you have paid them to take of you and supply to you. I wonder if this is not such a straightforward situation as made out to be.

The only inherent rights you may have as a model are the right against misappropriation and the right of publicity. In the US these are state rights; but not all states, nor all countries, have laws granting/supporting these rights.

Any other right contrary to existing law would have to be transferred *in writing (by contract). That includes your use of the images other than personal, and the photographer's commercial use of the images.

It is within the photographer's rights to watermark the images provided; it is considered to be part of copyright management. And it is generally a violation for you to remove the watermark (USA/UK/etc); doing so has significant penalties of its' own in the US (DMCA violation).

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*some rights could be transferred by inference (e.g. verbal contract), but that can be very messy/uncertain.

I think that it depends on which country You are living and do You have a professional status at any organization. In my country, when photos are paid and customer have those photos then customer have right to give free those photos to anyone. But photos can't resell or modify, for example removing your stamp isn't legal.

This is simplified version of your rights to the photos You have taken, edited and planned.

-Tomi Karjalainen