The decedent died intestate (without a will)
To answer your question, what you're asking about is simply an Application to Appoint Administrator, though different lawyers will sometimes use different titles. The point is, it isn't as much a form as it is a request. That written request must include some very specific facts regarding the decedent and his or her heirs. In order to be entitled to make the request, you must have some interest in the decedent's estate. In order for the court to grant the request, you'll need to prove (among other things) that there is a need to appoint an administrator.
The broader question is why you might want a third party appointed to the job, and whether you're thinking of an individual that is known and agreed upon by all of the heirs, or an attorney that the particular judge is familiar with. If you have an interest in the estate, you need to visit with a probate attorney to better understand how you might protect that interest. In simple terms, even though probate might be thought of as routine, it is not an area of law that you want to try to navigate by yourself or learn on the fly. Best of luck.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should never rely on this answer alone and nothing in these communications creates an attorney-client relationship.