Apparently, your question was not clear enough to @nancy2 .

An estate MAY have to file (a) an estate tax return (Form 706) and (b) annual fiduciary income tax return (Form 1041). 

Still, Form 1041 is NOT definitely (as you stated) required.  Read the 1041 instructions on "Who Must File".

@nancy2  interpreted your question as one about the TX version of Form 706.     

I don't have any TX estate or trust, so, I don't have a definite answer for you.  I like to clear my head before diving into work, and I'm helping you to get this question on Page one before it gets buried.  On April 9, only the lucky few would go past Page 2 in this forum.

In my e-library, I have a pdf file titled 

Residency and Source Income Factors for State Income Taxation of Irrevocable Non-Grantor Trusts

It's a list for state tax issues for trusts for many (all?) states. 

For TX it has one line:

Texas (0%)  No income tax imposed on trusts.

Perhaps a TX practitioner could verify no TX fiduciary income tax form is needed for a TX estate.