Good afternoon Isaias,
Thank you for the additional information.
You are very, very fortunate that you only filed for the partnership with the city, and because you are not a same sex couple, you didn't qualify to file for a CA Registered Domestic Partnership.
A city registered domestic partnership is not considered a CA domestic partnership unless you also register with the California Secretary of State. And it is ONLY the state domestic partnership registration that invokes all the same protections to each partner as married couples enjoy---including community property.
As you are not registered with the state, and you are not married, and the real property is in your name, you may seek to evict this person after giving them notice of the termination of their tenancy---30 days if they have lived there less than 1 year, and 60 days if they have lived there more than one year.
They do not own half of the property, nor are they entitled to half of the assets acquired during the partnership---including your property.
The state does not treat this break-up as dissolution or the termination of a California Registered Domestic Partnership. Instead, you are treated as roommates would be. Each of you is entitled to take what you paid for during the relationship, and neither of you will owe support to the other based upon the ending of the relationship. There is no division of property, as there is no community property in the first place.
In terms of preparing for the coming child support case, there is nothing that you need to do, proactively. If she applies for support, it will be based on each of your incomes, and as a general rule, you can expect to pay between 15% and 20% of your income to child support for one child.
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