For the third time of trying.
Fellowes of Dagenham can find a fair amount of information by looking at the blue box on the Answers main page entitled Find a Question. Look at topics where you will see Smoking. This will allow you to read a range of questions and answers on this topic.
If anyone wonders why the answers sometimes get sarcastic, read the above question!
If by "on board" you mean whilst walking the plank then the answer is YES.
Look at the blue box on this page entitled Find the answer. Select topic and scroll down. Click on smoking.
You will see plenty of previous discussions on this topic.
In addition, most cruise lines will state their smoking policy on their web sites. However, it is best to check the current policy when you embark on your cruise.
Now for a sensible answer.... since you do not specify which cruiseline you are referring to its difficult to give you anaccurate answer. Cruiselines are reviewing their smoking policies but generally speaking you can smoke on designated areas on open decks and in designated areas inside(on some ships) Thomsons for example currently do not allow smoking anywhere inside their ships although their recent brochure seems to have relaxed this. Some allow smoking in cabins, some not, some allow smoking on private balconies, some not. Read the policies on smoking for the cruiseline you are thinking of booking.
Look at the blue box on this page entitled "Find the Answer"
Scroll down to smoking. Click on this and yopu have access to a number of questions on this topic.