In a final attempt to keep her partner, said prosecutors, Carty plotted to kill a young neighbour - 25-year-old Joana Rodriguez - and steal her baby.
They said Carty told her boyfriend she was about to give birth.
Meanwhile she was said to have recruited a gang of men to break into Ms Rodriguez's apartment.
Promising them they could keep any drugs they found, Carty reportedly told the gang she intended to "cut the baby" from the young mother's body.
To back up their accusations, police say Carty's car was subsequently found to contain surgical scissors, a bag with a stethoscope and surgical scrubs; as well as a baby seat, diaper bag, baby food, baby clothes, and infant milk formula.
The gang abandoned her first attempt on 13 May after Carty got cold feet.
But on 15 May a witness saw her leaving a storage unit carrying a baby blanket and baby clothes.
Carty told the witness her baby was "home with its father", say the prosecution. The same day, Carty told her boyfriend and another neighbour she was going to give birth the following day.
The court heard that in the early hours of 16 May Carty met her accomplices at the apartment complex.
They all reached deals with the prosecution and got lesser sentences, avoiding the death penalty themselves to ensure that I would die
The door was kicked in and the men entered the apartment in which Ms Rodriguez, her partner, his cousin and four-day-old Ray were upstairs.
The gang bound the two men with tape, stole $1,000, and ransacked the apartment looking for more money.
While the break-in was going on, Carty telephoned one of the gang while he was inside the apartment and Carty was outside. The court heard mobile phone records confirm the call was made from her phone.
Carty was said to have entered the apartment to take the baby, while the gang stuffed Rodriguez into the boot of a car.
Later, three of the men met Carty at a storage lot where they transferred Rodriguez - who was not tied up at that time - to her car.
The prosecution says Carty later told her accomplices they could not let Ms Rodriguez go because she had "seen their faces".
On her instructions, one of the men taped Rodriguez's mouth and hands while she lay helpless in Carty's car trunk.
Joana Rodriguez "was alive and crying" when the car trunk was closed, says the Texas District Attorney's office.
The next time anyone saw Ms Rodriguez she was dead, with a plastic bag over her head. The court was told Carty was seen leaning over her open car boot.
Inside Carty's car police say they found baby items, medical scissors, ammunition and a stethoscope.
Police say Carty's fingerprints were also found in the rental car in which the body was discovered.
Ms Carty grew up in St Kitts, where she became a primary school teacher
Said Carty in a personal statement issued from her death row prison cell: "I was framed by three men who kidnapped my neighbour and put her in the boot of a car where she suffocated."
Describing them as "notorious criminals" she says the men "tried to place the blame on me for something they had done, and I can prove that".
She adds: "They all reached deals with the prosecution and got lesser sentences, avoiding the death penalty themselves to ensure that I would die."
British lawyer Hugh Southey, who has campaigned for Carty's release and who has visited her in her prison cell, said the central flaw in the prosecution's case was that it depended on the evidence of acknowledged criminals.
"The evidence of these man was crucial. Without their evidence, no court would have convicted Linda Carty.
"The prosecution's contention that Linda would also seek to pass off a baby of a different ethnicity is bizarre.
Ms Carty is on death row at Mountain View Unit women's prison, Texas.
"She would have had to have been delusional to think she could cut a baby out of its mother's body with a pair of scissors. She is a very intelligent woman."
Campaigners also point out that some of the evidence against her given by her boyfriend should have been ruled legally inadmissible.
Human rights group Reprieve says Carty's death sentence should be lifted because of her "catastrophically flawed trial".
"The prosecution case was later found to contain multiple inconsistencies and to be based on the testimony of career criminals who avoided a possible death sentence by framing Linda."
The group also says Carty's original defence lawyer failed to present an adequate defence.
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