How is procreation handled in Eclipse Phase? Given that morphs are highly interchangeable this heavily shifts the normal perception of how passing on your genetics would work. Also can infomorphs reproduce? I realize that right now population wise there are many, many infomorphs sitting in storage so the need for "new" people can be met. However the need to procreate would still have a hold on some portions of transhumanity. It's been awhile since I've read the core rules so I cannot remember if this is addressed there or not.
Greg Egan's Disapora starts with an infomorph's birth (orphanogenesis) if you were interested in reading it. Since bodies are irrelevant, the mix is a set of memories and education. Charles Stross's Accelerando is full of partial forks that get education till they are considered adults and different than the original.
Personally I would say that creating a child is like creating a memoryless fork, with strong characteristics (some random) and merging it with your partner's similar fork. You could add more forks into the mix: presto, you have a new blank ego that given different stimuli from its parents will evolve into something new.
Edit: I guess that this would be a good way to answer the Nature vs Nurture question: Does the nature take precedent or does educations and experiences? Many story ideas are just right there.
According to the Eclipse Phase main book (page 273), forking is still controversial. Given that, I would say that forking for the purposes of procreation would be more so.
That leaves us with only two possible answers:
1) Cloning with editing (as Ichoran states).
2) Morphs specifically engineered for the purposes of copulation and gestation. These would, in all likelihood, be very expense and/or only available to the very well-off. Each model (male and female, since it does take "two to tango"; or does it?) would be engineered for maximum fertility and guaranteed (or your money back?) to produce the desired number (twins, triplets?) of offspring. Since just about anything is possible given the level of genetic engineering, the morphs could come in exotic varieties as well: reproductive octomorphs, furies, whatever, would all be possible.
Of course, the bioconservatives still do it the old fashioned way.
Morphs are expensive and most people do not have the ability to switch morphs often. In addition I guess that humans didn't naturally evolve any further, thus there should be some primal urge to procreate. And that would happen as it happens today. Interesting would be, if you could get out of your morph if you are pregnant or if it is morally not allowed (like too much forking is not allowed more than by social standards than by technical limitations). And then there is the question when children are allowed to switch their morphs and what happens with a child that gets into a morph with a fully developed brain (or an adult into a children's body). After all brains are only finished with the age of 25.
Without having read the rules (but knowing a lot of genetics), I can offer that genetics ought to happen the way it always does: if genetically modified transhumans have not been modified so much that they can't procreate, their offspring will have half of each of their alleles just like always. That is, it would be the alleles of the currently occupied bodies, not anything to do with the mental host at the time. (Let's leave aside for the moment the possibility of further genetic modification after fertilization.) Given the level of genetic engineering in the setting, it's not at all clear to me that sexual reproduction would be favored over cloning with editing.
Also, since infomorphs are digital, genetics would not play a part. However, why would one need more beyond what one transferred in from those who were originally transhuman?