They can only petition the Federal government to accept the new states and their suggested borders. The state can not do this without the United States government accepting the break-up.
"New States may be admitted by the Congress into this Union; but no new States shall be formed or erected within the Jurisdiction of any other State; nor any State be formed by the Junction of two or more States, or Parts of States, without the Consent of the Legislatures of the States concerned as well as of the Congress."
Article IV, Section 3, Clause 1
What you say is true but, I believe Texas has the right to subdivide into 4 states, should it choose to, in accordance with its original charter accepting it into the union.