When a female conceives (regardless if birth occurs or not) there is lateral transfer of genes from the foetus to the mother. The mother becomes genetically tailored to the father and has the fathers DNA in some of her cells. She has a mosaic cellular structure.

Further if she later has a different partner she gains some of his DNA as well and so on.

In turn she can pass her acquired genes on vertically to her future children.

Therefore if you have children with a single mother

  1. You will never be as close genetically to the mother as you would've been with a virgin female

  2. You're children will inherit DNA from her previous partner/s

References

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC383270/

http://m.bloodjournal.org/content/120/3/505.long?view=long&pmid=22627770