The day you turn 18.
However, you can only take things that you given to you by inheritance or gift.
You will need to be able to prove this.
If your parents don't want you to take an item, such as a computer, your clothes, furniture, your phone, etc. then you cannot take it.
You can call your local sheriff and/or constable and discuss this matter with them. They are the local policing authorities that handle this matter regularly. They can make sure that the 18 year old exits is peaceable.
At 18, a person is an adult in the eyes of the State of Texas. An 18 year old for civil purposes is an adult. For criminal purposes, it is 17 years old in the State of Texas -- thus the confusion.