Marriage imparts ownership, for tax purposes. If you were married, then only one spouse needs to be on the title, even if the home is sold after the divorce.
If you were never married under any theory (registered or common law), then the home only belongs to the titled owner. In most cases, only the owner reports the sale and takes the exclusion. You probably have nothing to report on your return and you may not even have legal claim to any money. If you are breaking up your partnership, then your share might considered the same as a distribution due to a divorce (but that depends on the laws of your state), or it might be a gift from your partner to you.
I think you need professional legal/tax advice.
