According to Boat International, "the design for what would become the world’s most talked about superyacht bubbled into Starck’s mind at his home in Burano, Venice, in 2004.

Builder Blohm + Voss issued a press release in December 2004 identifying the vessel as Project Sigma,[1] which was how it became most commonly known during her construction.

[13] It was also stated in the press release that the owner of mega yacht Pelorus, Russian billionaire Roman Abramovich, was not the customer behind Sigma.

Nevertheless, because Pelorus was undergoing a concurrent refit at the same shipyard, and because both projects shared the same management company, there was continued speculation that the two vessels had a common owner throughout A's construction.

[7][9] Project Sigma was given the hull number 970 (she was the 970th build by Blohm + Voss), it was decided that construction would take place at Howaldtswerke-Deutsche Werft (HDW), a sister yard in Kiel also owned by B+V's parent, ThyssenKrupp Marine Systems.

[29] Once delivered, A's maiden voyage took her to Kristiansand in southern Norway, where Andrey and Alexandra Melnichenko collected three Claude Monet paintings they had recently purchased.

[30][31] When completed, A was the sixth-largest privately owned motor yacht in the world,[11] although by 2011 the construction of newer and larger vessels had relegated her from the top ten.

[29][33][34] A is powered by two MAN RK280 diesel engines providing approximately 9,000 kW (12,000 hp), sufficient to give the yacht a maximum speed of 23 knots (43 km/h; 26 mph).

Reportedly, security is tightly controlled, with 44 mm (1.7 in)-thick bomb-proof glass in the windows, over 40 CCTV cameras, motion sensors, biometric fingerprint/keypad entry for restricted areas and a rumoured escape pod in case of emergencies.

Jonathan Beckett, chief executive of London yacht brokers Burgess, was initially skeptical, but changed his mind after seeing the boat in person in the Caribbean: "I have to say I was impressed.

"[32][40] And writing about the world's biggest mega yachts in The New York Times in 2011, Nazanin Lankarini argued that A was "even more desirable [than] her larger sisters by virtue of lines reminiscent of a nuclear submarine".

"[42]"I'm all for innovation — as I've said before, the rich are free to spend their money as they like, including by building ugly boats that cost hundreds of millions of dollars.

[43] The Wall Street Journal's Robert Frank was initially also an outspoken critic, calling A "one of the ghastliest megayachts ever created" and "more like a cruiser for Darth Vader's navy than a family pleasure boat for the Mediterranean" when she was launched.