As long as your ex’s name is on the title to the house, he has a right to half the equity in the house, even many years later. This really is not an aspect of family law, but property law - if a piece of property is in your name, you don’t just lose it because you’re not around for many years or because there was a family law issue involved.
If the matter went to court, you could argue that your ex is not entitled to half the equity for a number of reasons - say, you’ve put improvements in the house or your ex would be unjustly enriched by getting half. You’d probably have some success with this especially if your ex hadn’t been around for many years. But it would be an expensive legal case, you’d have to do all the work to prove why your ex isn’t entitled to half the equity, you may need to produce receipts for improvements you’ve made, and more.
Also, as logicalvelocity said, you could never sell the house without your ex’s permission. If you needed to move quickly, your ex may be able to pressure you into an unfair settlement, just so you can get your equity out of the house quickly.
It would be best if you had a separation agreement done about this, as the agreement would include provisions that release you from any liabilities to your ex. However, at the very least, get the home transferred in your name.