Since the Trope Repair Shop is full, I guess I gotta ask here. This trope seems to encompass several factors that are getting mixed and matched in the examples:

• 1. The woman who wants to mate with a specific man so he can father her children.
• 2. A race is practically infertile, and they need some genetic material from outside the population to fix things.
• 3. The culture is basically female, and the limited (if there is one) male population just can't ensure enough genetic diversity. Ergo, any man from "outside" that wanders in is going to be desired.

I think the key phrases are "only you" and "repopulate my race". Both need to be present to be this trope. Therefore Superman and Maxima, among other examples, don't belong. Maxima just wanted a strong, handsome mate. There weren't any indications that an Almeracian (that's her planet, Almerac) man wouldn't have been able to father her children just as well.

We may need to split the "we need more genetic diversity" and "we need more people, period" examples into their own tropes.