This is how "uniao estavel" is known through out the Anglo-Saxon world. See article from Wikepedia:

A civil union is a legally recognized union similar to marriage. Beginning with Denmark in 1989, civil unions under one name or another have been established by law in many developed countries in order to provide same-sex couples with rights, benefits, and responsibilities similar (in some countries, identical) to opposite-sex civil marriage. In some jurisdictions, such as Quebec, New Zealand, and Uruguay, civil unions are also open to opposite-sex couples.

Most civil-union countries recognize foreign unions if those are essentially equivalent to their own; for example, the United Kingdom lists equivalent unions in Civil Partnership Act Schedule 20.

Many people are critical of civil unions because they say they represent separate status unequal to marriage ("marriage apartheid").[1][2] Others are critical because they say civil unions allow same-sex marriage by using a different name.

you can find this if you google Brazil stable union

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Note added at 51 mins (2008-10-17 15:02:04 GMT)
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see http://pubweb.fdbl.com/news1.nsf/c8abb103352ef95a86256e31008...

It's not just about same sex partners, which would be civil union