This question is far too general. Mental illness is such a broad term, for example, any 1st year psych student should know that ratio of mental illness to population size is at least 1.5:1. If anyone does not understand that, I mean to say, on average we all have at least one mental illness. The question you ask could be made into dozens or hundreds. I am sure there have been studies galore but a few ideas come to mind. How many kids grow up with parents with undiagnosed mental illness. Are there some illness' with better prognosis of good parenting. Is a depressed mother better than an angry father. What about alcoholics? What about mental illness vs. mental retardation or poorly educated, racist, homophobic, agrophobic, work shyness and so on. The diagnostic manuals for mental illness, the DSM being one, I was prone to reading this when I worked in a rehab. The book is huge! Reciting it would have to be near Pi. On the other end, what facts are certain in adoption? A child needs a home, what options does the child have? Each case should be decided on what is best for the child not to give a fair go to would be parents.