I don't know if there is a more precise, formal jargon for this, above is my lay person's suggestion.

I understood 'patrocinio' as the action itself, handling the process, nothing to do with sponsoring which, in my lay understanding, would mean that the law firm would pay themselves for the lawsuits! (but, if that's the case, I want their name!! ;-) that's a heavenly lawyer ;-)


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Note added at 6 hrs (2007-10-02 17:48:40 GMT)
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"marlcurtis: Some lawyers do it for free, it is called pro bono services."

the term asked is "patrocinio," not "pro bono" which exists in Portuguese usage in the original Latin as well.

To me there was nothing to suggest it's a pro bono description here, although that in itself does not rule it out, a look at the entire contract would probably solve the question. (Ben????)

and the only 2 examples of "patrocinio de um processo" on the web seems to confirm that you misinterpreted:
http://www.praetorium.com.br/?section=oab&id=109

46 - O Advogado SALVADOR DE SÁ, regularmente inscrito na OAB-RJ, após concluir o patrocínio de um processo de Inventário, no qual representava o inventariante e todos os herdeiros e administrava os imóveis do espólio, recusa-se a prestar contas aqueles clientes dos aluguéis que recebeu, sob ****a alegação de que os mesmo se recusam a pagar-lhe os honorários profissionais devidos.**** Pergunta-se: Considerando-se que SALVADOR DE SÁ é primário, a qual punição disciplinar estará ele sujeito na hipótese?
a) Suspensão, pelo prazo mínimo de 30 dias e até que preste contas;
b) Exclusão do quadro da OAB-RJ;
c) Suspensão, pelo prazo de 30 dias a 12 meses;
d) Censura;

9 - Um Advogado ajustou verbalmente com seu cliente os *****honorários advocatícios de R$ 20.000,00 (vinte mil reais) para o patrocínio de um processo de inventário.***** Concluído o trabalho profissional, aquele Advogado não conseguiu receber, amigavelmente, os honorários ajustados.
Pergunta-se: Qual a medida judicial correta para o Advogado receber aqueles honorários?


****honorarios devidos is not "pro bono." ****

Ben, I would ccertainly confirm with the client in any case, this is definitely a mistake you don't want to make in your translation!