I think it's illegal for them to ask about your kid and/or your baby mama.
I believe it's the civil rights act of (around) 1964 that prohibits discrimination based on many areas, including "age, race.. marital status".
There are lots of areas NOT included in this act that some people think should be included as illegal areas, such as weight, possibly being a parent.. can very obese individuals be required to buy 2 airline tickets if they can't fit in one seat, etc. In order to address the needs of parents, the Family Medical Leave act was passed; this allows specific amounts of time off from work (unpaid) in case of family sickness, adoption, etc. provided the employer has more than a certain number of employees and a few other conditions are met. From what I've heard about medicine, hospital environments would not be very sympathetic to a resident needing to take time off for this, however.
Captain Fantistic nailed it, though -- just because something is technically illegal, that doesn't mean it won't be asked, and there's almost no way to prove that a person is treated badly/denied a job/admission to med school/etc because they refused to answer a question -- an experienced interviewer who is biased could say that they selected the individuals who seemed the best fit for their school and not mention the "illegal" question at all.
Back to "being a parent impacting med school eligibility" -- As a person in corporate & business environments for many years, a red flag for me is if a candidate brings up something in an interview that does not need to be there, such as a time a coworker did them wrong, how strongly they believe in their religion, how much time it takes to care for their elderly parents.. my concern would be if I hired this person, that they could hold a grudge, offend others with their prostheletizing, and require frequent time-off accomodations, respectively. All of these areas are reasonable, but if you tell me about them and another candidate is enthusiastic about how committed they are to their job and dedicated to furthering the company mission, guess which one gains the upper hand in the interview process?