This is more of a family law question and I would suggest you consult with a family law attorney.
A deed creates a presumption that the person on the deed is the owner of the property. The presumption can be rebutted by external evidence. You will need to start compiling paperwork to prove your case -- that none of his money was contributed to the mortgage, property tax or insurance; and that none of his money was contributed toward any capital improvements. But even then, I can't say that he might not be entitled to a portion of the equity under the arcane rules of family law.
Depends on a lot of different factors to be able to answer that question. However, you should consider that all of the income you earned during the life of the marriage, absent a valid prenuptial agreement was the community property of your spouse. To that extent, half of the mortgage payment you made on that house he would be entitled to a credit for those moneys. What remains to be determined ultimately is whether during the life of the marriage does the evidence show that he intended the home to be your separate property, or was it his intention that he intended that you hold the home in trust for both of your benefit. Given the long-term marriage and absent any other factors that you have mentioned it is likely that if he obtains representation, he is like to receive a benefit which may include having an equity interest in the home to the extent of his community property contribution he paid through you into the home. Some judges would go as far to say that he acquired a full interest in the home. But other evidence is needed, such as who put the money down for the house when it was bought, who paid closing costs, did he live in the home..... etc.
I agree that you should obtain the services of a family law attorney in your community to help you. I know a very good one in the Inland Empire. His name is Jeff Nadelman, if he is still practicing. His spouse was also a family law attorney who may still have the same last name.
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