The orders are here and here.  Michael Graczyk had has this story earlier for AP.  (The same link now points to an updated story.)

Jesse Joe Hernandez already was a convicted child sex offender when he was arrested for the horrendous beating in 2001. Karlos Borjas [age 10 months] had a skull fracture amid bruises to his head, thigh and abdomen when he was taken off life support after a week in a Dallas hospital. His 4-year-old sister also was attacked but survived with swelling and bruises on her forehead, eyes and behind her ears.

"I just remember all the bruises and tubing," recalled Howard Blackmon, a former assistant Dallas County district attorney who prosecuted Hernandez for capital murder. "He beat the little boy senseless and beat the sister, too."

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[Hernandez's lawyers'] appeal to delay the punishment argued that trial lawyers for Hernandez should have pursued evidence that the boy "likely would have lived had he not been prematurely removed from life support" because he had toxic levels of the barbiturate pentobarbital when life-assisting machines were turned off, according to Hernandez's attorneys. Ironically, it's the same drug Texas prison officials now use in the execution process.

Something like, "Even though I beat a 10-month-old baby to death, the doctors might have been able to save him, so it's not my fault."  Yeah, that would have gone over real well with the jury.

Update:  Graczyk reports the execution has been completed.