If the deceased had a fully-funded living trust, do I need to do anything?

Yes.  A common misconception is that because a fully-funded living trust can be used to avoid probate, there is nothing to be done.  However, while the added work of a formal probate process is not needed, there are still tasks to be completed, such as obtaining a taxpayer identification number for the trust, updating the titling of assets, settling any final debts and expenses of the estate, and final tax returns.  The trust agreement will then include provisions on what should be done with the assets next—such as outright distributions or distributions to certain sub-trusts.