Ordinarily, property brought into the marriage is considered separate property. Whether it *becomes* commpunity property during the marriage can get a little blurred. For instance, the fact that you paid all the bills *may* make a difference, but then again, maybe not, as your income while married in AZ is usually considered community income. What is then purchased with that community income (as in, your house's equity via mortgage payments) may make the house communuty property. Also, if you lived in the home as a couple and/or have kids may affect the outcome.
If you can have the house deemed separate property, she probably won't be entitled to 50% of the equity. If it's deemed community property, she will be entitled to a fair division of that marital asset.
Another consideration: Does your STBX even want the house/equity division? She may accept that it's yours and leave it at that.