From the following Argentine Government page, "Union convivencial" appears to be an umbrella term for life partnerships between persons of all genders.

"¿Qué es la unión convivencial?
Es la unión afectiva entre dos personas que no se casan pero conviven y comparten un proyecto de vida en común durante un mínimo de 2 años.

Código Civil y Comercial de la Nación, Art. 509."
https://www.argentina.gob.ar/justiciacerca/vivimos-juntos


"Life partnerships involve the same commitment as that of civil marriage. Life partnerships involve the same core ideas and reciprocal duties of support as that of a civil marriage.

Life partnerships differ in that there is no legal recognition for a life partnership under any legislation."
https://www.vandeventers.law/Legal-Articles/entryid/312/marr...

There's also the term "cohabitation", but I'm not sure this Argentine definition necessarily implies living together.

"Cohabitation is an arrangement where two or more people are not married but live together. They are often involved in a romantic or sexually intimate relationship on a long-term or permanent basis."
https://en.wikipedia.org/wiki/Cohabitation

I would say

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Note added at 14 mins (2020-01-10 00:04:02 GMT)
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Nonmarital Unions, Family Definitions, and Custody Decision Making. Relationships that have not been formalized by marriage but that function like marriage ...

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Note added at 17 mins (2020-01-10 00:06:44 GMT)
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You could hypenize it but not really necessary

Thirdly, qualifying an unmarried couple's relationship as marriage would result in the application of the conflicts rules for marriage to non-marital unions, which ...

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Legal Qualification of Non-Marital Unions A. An Element of Personal Status 1. Non-Marital Cohabitation a) A Personal Relationship b) Significance of Article ...

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and "hyphenize"

As a title for a degree subject

U.S. Cohabitation Law: Still Separate and Unequal | Institute ...
https://ifstudies.org › blog › us-cohabitation-law-still-separate-and-unequal
Jun 25, 2019 - Occasionally, a story appears about a state that still possesses a law against cohabitation and has undertaken a rare enforcement action.

Common-law marriage, also known as sui iuris marriage, informal marriage, marriage by habit and repute, or marriage in fact, is a legal framework in a limited number of jurisdictions where a couple is legally considered married, without that couple having formally registered their relation as a civil or religious marriage.

common-law marriage differs from statutory marriage as follows:

There is no marriage license issued by a government and no marriage certificate filed with a government
There is no formal ceremony to solemnize the marriage before witnesses
The parties must hold themselves out to the world as spouses (this is not a requirement of statutory marriage)

Most jurisdictions require the parties to be cohabiting at the time the common-law marriage is formed. Some require cohabitation to last a certain length of time (e.g. three years) for the marriage to be valid. But cohabitation alone does not create a marriage. The parties must intend their relationship to be, and to be regarded as, a legally valid marriage.