How do I know if I should renounce all right and claim as a residuary beneficiary in my uncle''s will?

You have the right instinct to be cautious.  The renunciation is not to give up your inheritance under the will, but to give up your right to serve as the Administrator of the estate.  Because your uncle did not do new will after your aunt and uncle were divorced, she is named as executor as his wife, and therefore not eligible.  Most likely the will did not name a back up if she was ineligible, so right now no one is able to serve.  She is sending you this paperwork because as a beneficiary you have a right to serve as the administrator of the estate, and she must get your consent that you are giving up this right and agreeing to allow her to serve.  Administrator CTA means administrator appointed by the court.  If there was some one named in the will, they would be the Executor.  I'm not sure why she would want to serve as administrator, but its probably not a good idea since they were divorced. As the administrator, you can be paid a commission for the work hat is done, and your attorney's fees would be paid from the estate. If you want to be the Administrator, you can refuse to sign, and apply to the court to serve as Administrator, or one of the other beneficiaries can apply.  You absolutely have control over this and I would be happy to help you.  Feel free to contact my office.