#4 - A litter and also a stain problem (if you stub out a cigarette on the stairs, the floor, or the wall you'll leave a stain). The only possible way to avoid it would be to grind the stub into a shoe sole or your partner's palm and that would be difficult to implement.

I was actually going to post the same thing about BE. :-)

In this special context it doesn't seem to be the same thing though.

The OP text is a strangely particular prohibition. The wording seems to imply that smoking a cigarette and also putting it out is fine (with the exception of stubbing it out against a surface). Perhaps it is a stairwell that allows you to hold/smoke a cigarette while passing through.

There are different ways of putting out a cigarette without stubbing it out against a surface of the building (which seems to be the relevant distinction).

- Using another surface (like a shoe sole)

- Taking the cigarette outside to put it out there

- Putting the cigarette into a provided receptacle like an ashtray (that's filled with sand for example) 

Kathy, if you are not certain about what is or isn't prohibited, you'll probably do best to translate exactly and not interpret the original to mean "Smoking is prohibited in the stairway/stairwell".

It shouldn't really be an issue that "It is prohibited to stub out cigarettes" or "It is prohibited to put out cigarettes against a surface" sound strange. I've asked some native speakers of German and they say the original sounds strange too and we have to presume that this has a reason.

If you know for a fact that smoking as a whole is prohibited there, then a simple "No smoking" sign will do.

A change in the law wouldn't make any difference, since the prohibition in the OP is not a statutory ban, but a rule of the house.

BTW, in the 'Columbo' episode 'Caution: Murder Can Be Hazardous to Your Health' the way the murder victim put out his cigarettes is a vital clue at the crime scene.

But it explains the puzzlement people feel about the fact that it seems to be okay to smoke in the stairwell, but not to stub out cigarettes. I'm always amazed how thoroughly I've got used to the smoking ban(s) - it's almost impossible to imagine, for instance, that only 15 years ago I not only used to smoke but used to smoke in an office. Like almost everybody else on that floor. It seems absurd nowadays.

So walking around inside a building with a burning cigarette wouldn't have raised any eyebrows. Stubbing them out, however, would have (see #5)