Why did China only claim Tibet, but not Nepal or Bhutan?
Afterall Nepal was under the influence of Qing Dynasty during 1800's.
Sino-Nepalese War
Nepalese–Tibetan War
And Bhutan was a part of Tibet throughout much of its history.
History & Politics
History of Bhutan
Given Nepal's and Bhutan's location, they would have been of immense geo-strategic value to China, as China could have directly connected with Bangladesh and cut of India from its north eastern territories.
So, why is it that China never laid claims over Nepal or Bhutan but still does lay claim over territories like indian occupied Tibet?

Ritwik Banerjee, Sanskrit enthusiast
Answered Apr 30, 2015
Your assumption is incorrect.
I. BHUTAN
China does claim parts of Bhutan. These is a boundary dispute between the two nations that is a small fraction of China's international land border, but a significant portion of land for a small nation like Bhutan.
Officially, the claim into Bhutanese territory follows a plot that is now so standard that it warrants no more than stifled yawn:
That piece of land you think is yours was a part of another land that used to belong to Tibet, which used to belong to China a couple of hundred years ago according to some documents maintained by the then Emperor's court in Beijing. If you disagree, you're a dumb Western propaganda!
(Never mind the fact that Tibet can make the exact same claims about Yunan province in China, but, well ... they don't have the military to back up that claim. And also, that's not the point of this answer.)
But the strategic reason behind this claim is different, and from India's perspective, far more sinister. Due to the way India was partitioned in 1947, she was able to retain a very narrow sliver of land that connects the north-eastern states to the rest of India. This piece of land, the
Siliguri Corridor, is often called the
Chicken's Neck, and rightly considered to be one of the most vulnerable points in India's political geography. Here is what it looks like (take special note of the strategic importance of Nepal and Bhutan in this picture):
Also note that the region in the upper right of this picture (above the dashed line) is Arunachal Pradesh, an entire state of India that China is claiming as Chinese territory. (Never mind that the Tawang monastery, which paid homage to Lhasa, received voluntary gifts as opposed to mandatory taxes from only the 13% of the population that was Buddhist. Historically, Arunachal Pradesh was always a mix of traditional tribal religions and Hinduism.)
Now let us look at the territory dispute between Bhutan and China. Here is a snapshot taken from Google maps (please open it in a new tab for a clearer and magnified picture):
Note that geographically, these regions are
not in the Tibetan plateau, but very much a part of the higher reaches of the Himadri range of mountains in the Himalayas. China has little interest in Jakarlung and Pasamlung, at least when compared to the Doklam plateau. The major objective is to "resolve" the dispute in Jakarlung and Pasamlung in exchange for a bigger slice of land from the Doklam plateau completely given away to Beijing.
Why so interested in expanding claims around the Doklam plateau?

Because it enables China to broaden the strategic Chumbi Valley, exposing the Siliguri Corridor to an even more direct Chinese threat [1].
In the event of a confrontation, the PLA can simply cut off the entire north-eastern India and easily take control of Arunachal Pradesh (and perhaps even more ... maybe a thousand years ago some other part of India was a part of a kingdom in Arunachal Pradesh!).
I. NEPAL
The only reason China is currently not claiming parts of Nepal is because there is tug-of-war going on between India and China for influence in Nepal. And so far, China has been extremely successful in reducing Indian influence. A significant portion of the Nepalese people vehemently hate India ... and while the people of India don't understand the reason behind it, a detailed analysis of New Delhi's actions (or lack thereof) in Nepal shows that this hatred may be partly justified.
China saw this anti-India sentiment as an opportunity, and has exploited it with astonishing success! Now, however, if they start claiming parts of Nepal's territory, all this soft power will simply vanish, and Nepal will turn to India in order to counter the Chinese threat -- exactly as it had turned to China to counter what it saw as intrusive actions of India in Nepal.
In fact, this to-and-fro between China and India has been going on in Nepalese politics even when India was still British India. It resumed with new enthusiasm after the Chinese annexation of Tibet. India, however, was rather obtuse and instead of gradually increasing real influence in Nepal, repeatedly acted in ways that could be construed as interfering in Nepal's sovereign matters. This is what led to the anti-India sentiment I mentioned earlier.[2]
I personally believe that China will, indeed, claim the Mustang region of Nepal in the near future. After all, the people of Mustang speak Tibetan, and consider themselves to be Tibetan in all socio-cultural dimensions[3, 4].
The pretext will be the same story as before:
This was a part of Tibet, and Tibet was a part of China. We don't care if Tibetan documents show otherwise. Qing documents are mightier because ... umm ... well, because you're a Western propaganda!
But doing so now would be premature, and will definitely undo the inroads they have made into Nepal over the last three decades. Unlike India, I find it highly unlikely that China will act bluntly until its influence in Nepal is indisputably strong.
[1]
In Bhutan too, Chinese grab land
[2]
China–Nepal relations
[3]
The Unexpected Familiary: Finding Myself in the Kingdom of Lo (Mustang)
[4] Kurtis R. Schaeffer.
Himalayan Hermitess : The Life of a Tibetan Buddhist Nun. Oxford Univ. Press.
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