Oh, they all fit this definition, but the mutation isn't always spontaneous.

For example, cervical cancer is often caused by HPV, which is why school-age girls are routinely immunised against it in the UK.

I'd be suprised if any cancers were completely spontaneous rather than us just not knowing what causes them.

Let's break that down a bit:

There are many genetic determinants of whether you will develop a cancer, or a particular type of cancer. People with FAP, or HNPCC, or other proto-oncogene mutations such as BRCA2 will have a very high probability of developing a specific cancer in their lifetime.

But the mutation that leads to cancer is a spontaneous event, that is allowed to occur due to a failure of cellular regulation.

There are many viral causes of cancer, as OP mentions HPV for cervical and penile cancer. Other strains of HPV are linked to SCc (a form of skin cancer) and throat cancer. Hepatitis C will cause liver failure and Hepatocellulr carcinoma in approx 20% of infected patients. Infection with H. Pylori can predispose to gastric carcinoma.

Additionally exposure to various 'environments' can lead to cancer - if you have GORD you can develop Barett's Oesophsgus due to the gastric acid irritating lower oesophageal mucosa, which can predispose to oesophageal cancer. if you are an alcoholic you can develop cirrhosis and later Hepatocellular carcinoma due to prolonged inflammation in the liver. If you are pale skinned and live in a sunny climate you are at higher risk for melanoma and if you eat a poor diet you have an increased risk of colon cancer. Smoking and exposure to smoke can give you lung, oropharynx, stomach and bladder cancer.

As of yet we have no idea what, of any, are associations for many of the Brain, bone or Kidney cancers (excluding some toxins for kidney cancer).

Possibly there is no cause.

But in all of these cases, the mutation still arises 'spontaneously'. That is, we all have a probability of developing a mutation that can cause cancer every time a cell divides in our body. In people with Li-Fraumeni syndrome, who have a mutation of p53, almost everyone will develop cancer by the time they are in their 40s. So we know the rate of gene knockout is quite high over our lives, and if it wasn't for immunosurvielance, we would likely fall prey to cancer much faster than we do anyway..

All having a risk factor or infection does is increase the probability that a cell will 'spontaneously' develop a mutation that will make it cancerous, and having more of these mutated cells arising increases the chance that one will evade immunosurviellance and continue to grow and expand.

Bottom line: as a doctor I see all cancers as spontaneous. You could say that x causes y, and in many cases there is a strong association, but in no case is that association as strong as, say, life leading to death, for which there is a correlation coefficient approaching 1.

While I appreciate the information and agree that it's pragmatically spontaneous my point was that I was suggesting we'll find that it won't be the case if and when we gain a deeper understanding, which we may never do.

I don't know but the sarcoma the articles says is a symptom present in the last stages of AIDS, when the body is covered with brown "patches" - mostly in the back. Other doctors were investigating other issues at the time, like a strong TB. But it took time for all this different specialists see it was one illness.