2 people buy a home. Both are on the mortgage but only one is on the deed. 5 years later the house is refinanced and now both are on the deed and mortgage. One year later one walks away and for the next 6 years the remaining owner makes the payments. Who gets what portion of the equity? There was no equity when one walked away. The person who walked away is demanding the house be sold and wants 50% of the equity.
According to Time:
If both partners sign the title as tenants in common, then each owns a specified percentage of the property. One person may own a 60% interest, while the other owns 40%, for example. This split is specified in the deed. (Emphases mine.)
There is another form of ownership call "joint tenants". This is where everything is shared equally.
First find out what kind of ownership you have, then consult an attorney if you feel that legal action might be needed to resolve your issue.