The two were sister ships. They were built to the same plans. Britannic was the most different of the three. The Olympic & Titanic had the exact same dimensions. Titanic simply had more enclosed space than Olympic, which was factored into her gross tonnage figures (tonnage was not weight, but a measurement of internal space) and made her the "largest" liner in the world.

Olympic was the world's largest ship for about two years (discounting Titanic's brief reign) until the Imperator came out in 1913.

The dummy funnel was used for ventilation and also exhausted smoke from the galleys.

Full power could still be needed while moving into port, so I doubt they would begin shutting down boilers at this point. The Hudson has very strong currents.

The aftmost stack was a dummy as far as the main boilers were concerned, but was still used for ventilation of other machinery - 'donkey' engines, cooking smoke, et c.

It is well known that No. 4 funnel on TITANIC was a dummy, and also that the three "sister ships" were not true sisters but differed in a number of respects, including principal dimensions; they might not be called sisters were they in existence today.

In this photo it looks to me like there is smoke coming out of No. 4 funnel, which in the most famous sister was a dummy. Does that mean this was a "real" funnel in OLYMPIC? Smoke is plainly to be seen above No. 1 and 3, with maybe a tiny wisp above No. 2. Isn't it at least a little odd that all boilers seem to be active as the ship is just maneuvering into harbor? While the ship's engines would be used in docking, with tugs to help, it doesn't seem that full power would be needed and letting some boilers cool off would be more economical of coal.

Is it possible the photo was touched up to show smoke where there was none in reality?

Since it was the Edwardian era, it would have been His Majesties Hospital Ship Britanic.

Although Olympic's two sister ships Titanic and Britannic had tragic ends, Olympic's worst event in her 24-year career was her 1911 collision with the British warship HMS Hawke in the Solent (the strait between mainland England and the Isle of Wight) when her captain ordered a turn that caused a collision with the Hawke, much to the surprise of the Hawke's captain (who probably muttered "amateurs!"). Repairs caused a delay in the completion of the Titanic and, when the all-better-now Olympic lost a prop blade sailing from New York in February 1912, a blade from the Titanic was used to replace the one that was lost, pushing Titanic's first/final voyage to three weeks later, very probably creating her iceberg collision destiny. The captain of both the Olympic during the Hawke wreck and the Titanic was Edward Smith (who died with Titanic).

The luckiest woman? That'd be Violet Jessop, a young woman who was a stewardess on Olympic when the Hawke collision occurred, a stewardess who survived Titanic and, while serving in World War One as a Red Cross nurse, escaped from Britannic when she sank in the Aegean Sea after hitting (it's thought) a mine.

By the way the rearmost (aftest?) smoke stack on all three of these ships was a dummy, to make the designs more balanced. The stacks were used for ventilation.

Here's Nurse Jessop in her Britannic uniform.

Because she was equipped and certified to carry the mail, Olympic's actual title (like Titanic) was not 'SS' (Steam Ship) but 'RMS' (Royal Mail Ship). Sister Bitannic was an HMHS (Her Majesty's Hospital Ship).
Many old photographs and film mistakenly identify Titanic but are in fact Olympic. The way to tell the difference between the two is the open promenade deck (below the boat deck) as seen here on the Olympic, which was enclosed on Titanic after Olympic customers had complained of the cold there.
According to author Walter Lord, after the Olympic was decommissioned in 1935, her interior wood panelling was sold off and used to decorate the interior of British pubs.

The Olympic class liners were quickly outclassed.

http://en.wikipedia.org/wiki/SS_Imperator

The three Imperator class ships also had far improved interior volume then any ship previous including the Titanic. They were the first ship to break up the exhaust into many smaller pipes. On the Titanic the funnel casing ran straight up the middle of the ship.

Google-Wiki has a very informative article on this ship. For instance, like the Titanic, when she first went to sea she was equipped with twenty lifeboats, enough for half the people on board. When White Star received public condemnation for this after the Titanic disaster, it scurried around and secured additional, second hand, collapsible lifeboats from troop ships, for the Olympic. Some were rotten and could not be opened. 'And so they went to sea once more, "Sensation" they for aye forswore.' (Apologies to W.S. Gilbert.)
In 1918, she sank the U-103, that was attempting to torpedo her, by colliding with it.
http://en.wikipedia.org/wiki/RMS_Olympic
http://www.youtube.com/watch?v=x6dB2RA8Kno

Because the Olympic was a sister ship to both the Britannic and Titanic, and the smallest of the three, but not by a lot. Olympic was the world's largest ocean liner between the time she was launched and 1934 or so, when the Queen Mary came into service, except for during the very brief careers of the two sister ships. Everyone knows about Titanic. Britannic was launched right about as World War One was starting up, and never served as passenger ship. She was put into service as a hospital ship, and struck a mine near Greece in 1916 and sank.

It would have saved James Cameron a lot of CGI work.