I do not know about California, but Texas is easy enough to research.
http://tarlton.law.utexas.edu/constituti...

Texas will NOT be five new states.
http://www.snopes.com/history/american/t...

http://www.tlc.state.tx.us/pubslegref/Tx...

Texas is, indeed, the state that feels most like a foreign country, but we are not going anywhere. Texas is in the Union, now and forever.

"Texas still operates under the 1876 constitution today. Because of its tight restrictions, it has had to be amended hundreds of times and is now considered to be one of the most disorganized and confusing of all state constitutions. In 1974, a constitutional convention met with much fanfare to draft a modern document. The convention ended in failure, and no attempt has been made since to replace the much-amended old warhorse."
According the Treasurer of the State of Texas
https://www.tsl.state.tx.us/treasures/co...

Moveover, if you check Snopes.Com the famous URBAN LEGENDS website, you will find that Texas will always be Texas, not five states.
http://www.snopes.com/history/american/t...

I guess we can agree to disagree. Your categorization as the People's Republic of Austin is telling. As to your generalization of the citizens of Houston as 'ignorant, redneck, fascist' tends to make me think you also may suffer from a myopic bias which lends itself to some mild vituperation. And if you would care to check those areas which I named for a proclivity to 'cling to God and their guns' (as one wag put it), you might find a pronounced desire for libertarianism. All in all, I'd say we probably won't agree on much but I'd still like you anyway. Oh, as to where I live, I live near Corpus, grew up in the RGV, lived in Irving and near Athens. Spent many years traveling the globe as a guest of Uncle Sam, halfway around the world, each way ( twice), including Viet Nam. Been an itinerant farm worker, short order cook, front line municipal worker, unemployed more times than I like. BA from UT-PA, Masters from UT-A in Public Administration, city administrator three times.

I don't know where you live, pardner, but here in the People's Republic of Austin, we are loyal to the United States of America. This is a liberal town, a university town, Democrat Party town. Sure, we have a lot of Ron Paul bumper stickers here. Sure, Alec Jones' Infowars comes from here. That is part of the mix. No way we want to jeopardize that. We like being Americans.

Houston? Sure, I mean aside from NASA, Houston is ignorant, redneck, fascist. Dallas? Big D is more like Hot-lanta than it is like El Paso or even Fort Worth up the road.

What I am saying, pardner is that you are guilty of confirmation bias. You see the facts that support your intended conclusion.

Texas has the legal right to secede, without anyone's permission. This right was afforded them when they joined the union as a republic in 1844. Texas also has the right to form its own army and navy, I guess, by extension, is own air force. Believe me, there have been a lot of rumblings in that direction for some time now.

Baloney. Thumbs down for silliness.
Cite the articles and clauses.
We operate under the Constitution of 1876.

Morever, the provision that Texas could subdivide into five smaller states was long ago abrogated.
http://www.snopes.com/history/american/t...

You do NOT understand it correctly. Texas is firmly and forever with the Union.
http://tarlton.law.utexas.edu/constituti...

Texas is in a tough position, then.

If I understand your initial post, Texas has reserved the right to secede from the United States...but only as an intact state. Separate Texan counties don't have that option, but may perhaps secede from Texas and form their own, new, state?

That would be answered somewhere in the Texas State Constitution, and I am the last to answer that!

Based on what I know about certain areas of Texas (and living here lets me have a diffident certainty), at least 80-85% of the state would go. Austin, Houston, possibly San Antonio, parts of Dallas and Ft Worth would favor the status quo. The Rio Grande Valley would probably opt to become a part of Mexico. It almost is anyway. IMHO, the greater part of East Texas, Central Texas, North Texas, Panhandle and West Texas would go. So, our problem is a bit different. We would have individual counties willing to stay rather than secede.

What about individual counties?

What is reported in the article is that this county wants to leave California, per se, and become a new state.