The answer depends on how the deed is titled.
I will assume that you are tenants in common. Absent a statement in the deed assigning percentages of ownership, she owns 50% of the property. Tenants in common are generally not liable for improvements made by the other tenant. Similarly, tenants in common are not liable for rent to the other tenant in common because one lives in the home - unless the tenant in common has been refused the right to also live there. On the other hand, tenants in common are generally liable for their half of the carrying costs of the home which would include the mortgage and property taxes.
Buying her out for $10K might be a good deal.
If she refuses to convey the property to you or to settle for a reasonable amount, you would have to file a partition action seeking a court to sell the property and for an accounting of the contributions and expenses paid by the tenants in common. That will cost you much more than the $10,000.
I am not a GA attorney, laws vary from state to state, therefore you should always consult a local attorney.
If this answer was helpful, please mark it as helpful or as a best answer. This answer is for general education purposes only. It neither creates an attorney-client relationship nor provides legal guidance or advice. The answer is based on the limited information provided and the answer might be different had additional information been provided. You should consult an attorney.
She owns half the house. If all she wants is $10K that is likely a great deal. Have a lawyer draft a proper contract and deed so this doesn't bite you later.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you (and am not your lawyer). Do feel free to call me at 404-768-3509 if you wish to discuss actual representation (the phone call also does not retain counsel; that requires an office visit and appropriate paperwork). In that a forum such as this provides me with limited details and doesn't allow me to review details and documents, it is possible that answers here, while meant to be helpful, may in some cases not be complete or accurate, and I highly recommend that you retain legal counsel rather than rely on the answers here. (You can also email my office at firstname.lastname@example.org . An email also does not retain my office, but can help you get an appointment set if you prefer not to call). I am happy to discuss possible representation with you. Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated Ashman Law Office as a debt relief agency that can help people file bankruptcy.