Hi Walter I dont know whether you got this already but here is a loosely translated version of what Andre said:

Hello to all, For the exchange I am the first Martins to answer of Portugal! To the best of my knowledge and belief, Martins (along with other finished Portuguese names ending in " s") it means son of Martim. In turn, Martim has Latin origin (probably proto-Roman) and means, coarsely, " Guerreiro" e " Nobre". Establishing the linking with the Roman God of the war, Mars. However, névoas of the time olvidaram more given concerning this name. They observe, also, the clientele of Algueirão-Mem Martins. The Martins name, according to Rui archaeologist Oliveira, probably originates from the name of the medieval knight who liveed in this region that Martim Escorso was called. Consequently, the name will be able to also come from the nickname of the children of this knight who had also lived in this region that they called " Martins". PS: Without a doubt that highest probabilities of terms will exist sanguineous affinities! With the best compliments, Andres Martins, Geógrafo