AZ LAW: NO DUTY TO RETREAT!
Arizona state law: there is apparently no "duty to retreat" when faced with violent criminal activity, and the use of deadly force is lawful when Citizens are attempting to prevent these crimes or to apprehend the perpetrators. 13-411. Justification; use of force in crime prevention
A. A person is justified in threatening or using both physical force and deadly physical force against another if and to the extent the person reasonably believes that physical force or deadly physical force is immediately necessary to prevent the other's commission of arson of an occupied structure under section 13-1704, burglary in the second or first degree under section 13-1507 or 13-1508, kidnapping under section 13-1304, manslaughter under section 13-1103, second or first degree murder under section 13-1104 or 13-1105, sexual conduct with a minor under section 13-1405, sexual assault under section 13-1406, child molestation under section 13-1410, armed robbery under section 13-1904, or aggravated assault under section 13-1204, subsection A, paragraphs 1 and 2.
B. There is no duty to retreat before threatening or using deadly physical force justified by subsection A of this section.
C. A person is presumed to be acting reasonably for the purposes of this section if he is acting to prevent the commission of any of the offenses listed in subsection A of this section.
You can run a search on the other statutes referred to at http://www.megalaw.com/az/azcode.php
I did a lot of research into the Arizona statutes myself and found this particular item. I also discussed this with Marine Inspector, who is a INS agent in Arizona, and we basically agreed that you could not legally perform a citizens arrest on someone upon the observation of their illegally crossing the border, as you could not be sure that it was a felony in commission - and a poster affiliated with one of the border groups in Arizona agreed that they only observe and report crossings, and save citzens arrests when they observe illegals breaking into a building and removing belongings, which raises the bar to a felony in progress. It's your choice whether you decide to confront and search someone who is a possible illegal - but IMO the safest, most legal approach would be to report them to the Border Patrol as the Arizona groups currently do.
BTW, I didn't see anything in Texas law that allows you to search someone trespassing on private land, but there's a lot of statutes to search and their search engine isn't too hot - can you provide a cite of that statute?