sex limited genome transmission
Is there any species (not just mammals) where most, or even all, of the genome is inherited in a sex-specific trajectory?


Here are a bunch of cases and specific examples that may interest you


There is a species of ants where both genders evolve to be able to reproduce by parthenogenesis (which means that males might be call females as well). In this species, the two genders mate together to create workers that do not reproduce! Therefore, when you look at the phylogenetic tree you can see that males and females are on two totally separate branches as there is reproductive isolation between the sexes in terms of fertile offspring. There is an article by L. Keller on the subject.
In the amazon molly, there are no males. But it is interesting because females need sperm to start the development of their ovules although they don't even use the genetic material of the sperm. Therefore, the amazon mollies need to find mates in sister species. In consequence, they imitate the females of the other species. There is a recent article from Hanna Kokko that investigate with a mathematical model how such system may be able (not cause the extinction of the amazon molly or of the sister species).
Sex-specific segregation distorter. Nasonia sp. may be an interesting case study
Haplo-diploidy. In ants for example, sons receive genetic material from their mother only. They are haploid.
if the rate of sexual reproduction is different from 1 then, females are responsible for more than half of the inherited genes in the next generation.


I apologize for the lack of references $\ddot \smile$