How to nominate successor trustee if all named successor trustees have died?

In general, you'll first need to look to the language of the trust document, which may contain a provision addressing this issue. Sometimes, trust language provides a mechanism whereby beneficiaries or a defined interested third party (e.g., creditor) may vote or nominate a successor trustee and who may (or more importantly, may not) qualify as the successor trustee. If the trust does not contain language addressing the appointment of a successor trustee, then look for a provision that permits the winding up or termination of trust when the trust becomes "uneconomical", or upon the agreement of all the beneficiaries. Finally, any interested party may petition a court of competent jurisdiction for the appointment of a successor trustee. In this matter, and especially because there is more than one beneficiary, I strongly suggest you consult with an attorney experienced in trust administration.

You first need to look at the trust. Most trust have a way of appointing additional successor trustees when those named are unable to act. If the trust does not have a named successor trustee or way to appoint one, you will have to file a petition with the court to have the court appoint a trustee to wind up the affairs fo the trust. In order to do this, I would strongly recommend that you consult with an estate planning lawyer familiar with trust administration. I can give you a referral in LA if you need one.