apoyar - is usually how we say "to support"..
Im not sure if "Mantenimiento" is correct, maybe "Mantener una familia". It sounds correct also...
I would say "apoyar una familia" though.....

Yes, you are correct. Soportar una familia means to put up with a family (which is often an important part of supporting a family, jaja). As you seem to know, soportar is a false cognate of support.

Thank you James for your answer....and yes, agreed estoy soportando la mia, jaja.

If you are looking for definition in a legal contex, the righ spanish word is MANUTENCION.
Se dá mantenimiento a una máquina; Se provee manutención a una familia.
ÿl mantiene a su familia, is correct, and the common form too.

Yes, Vernic indeed, thank you very much!!!! I got the Oxford and Collins on back order (hard copy and CD) cannot find the Real Academia just yet. Thought this site will provide some help in the meantime. Guess what? It did! Much appreciated. I think that I will still use the site as well, it is nice to get some feed back from "real" people.

If supporting is "providing what is needed by the family to live" then you should translate it as "mantener una familia".

Hola Greta. You will find it at: http://www.rae.es/rae.html
This is a very reliable source.

Don't forget the personal A! "Estoy soportando a la mia."

Hola Vernic:
Again thank you, now that will be a great help. Hasta prontito.

yes, indeed

I am not so sure, but I think that Support a family mean: Apadrinar una familia
support a family in third world=apadrinar una familia del tercer mundo
literally is Apoyar/Ayudar una familia

These are right about "Ayudar a una familia"; But, you can consider the other as true.
Ayudar is voluntary.
Mantener o dar manutencion is a moral or legal obligation, or may be for court order too.

yes
and help or support a family, boy or daughter in the third world is used Apadrinar

You are correct, but I think the more natural translation of apadrinar in that context would be "to sponsor."

I believe that support of family can be translated from both forms
Ayudar a una familia (unos vecinos que estan en apuros)
Apadrinar a una familia del tercer mundo (ayudar economicamente por medio de una ONG, etc...)
there depends the idea that wants to give the one who says it