If while backing out of a parking space I bumped into a pedestrian who is claiming an amount that surpasses my auto policy coverage, what kind of lawyer will I need?

I am assuming here that you were served with suit papers, correct?  ANd the claim for damages in excess of your policy comes at the end in what is called the Ad Damnun clause.  They claim millions?  This is a common statement made by plaintiff's attorneys and often done becuase under the law you are bound by the claim for damages made in that paragraph.  So they shoot high when often their proof can not sustain their claim.  Now, are you writing this question here because you got a letter from your insurer telling you that the claim is in excess of your policy and you have the option to hire your own attorney becuase they can only cover you up to the $50K and your laywer assigned knows that?  If you were insured then you are entitled to an attorney.  And that attorney has to zealously represent you in the suit no matter what your coverage.  It is his or her ethical obligation.  So you will be assigned an attorney pursuant to your policy that handles insurance defense cases on a regular basis. Let that attorney asses the damages alleged to tell you if you should be concerned that the verdict will exceed your coverage.  99.9% of the time it does not.  If your case is the exception, then you can consult an putside PI defense attorney.  Otherwise understand that the attorney assigned - and your insurer - have an ethical obligation to settle the claim within your policy limits. Good luck.