Answer

In the future, it would be good to spell out the question a bit more.
I assume you mean to ask what the law is when a couple gives a fertilized egg to be placed in another woman’s womb. The question is: who is the mother? I don’t know, but on intuitive grounds my inclination is that the owner of the egg is the mother, and the owner of the womb is the host (a surrogate = a hostess/host). She offers them a home and nourishment for the fetus, and nothing more. What I have seen in halakhic discussions is based on an anachronism, as though one could prove this matter from the Talmud and the Sages. I very much doubt that, since they were not aware of the biological details involved here. But of course, this is only an initial thought, and certainly in order to decide one would have to go through the sources and examine the biological issue and the like more carefully.