BAA has been trying to acquire the rights to baa.com, having missed out on claiming the site sooner.
The current baa.com describes itself as "a site for sheep and woolly resources" and features a range of curiosities suited to the sheep-minded browser.
According to the London Evening Standard, BAA has now served writs on those it alleges are running the site.
Get ewe
The paper says things turned nasty when site owner Tom Bourke, a British computer consultant based in New Jersey, upped the price of the domain name from £8,000 to £2m ($3.16m).
It says he complained that BAA was constantly introducing new conditions so he called the deal off.
When talks restarted, he increased the price "in line with the market and in the hope that BAA would just give up."
A spokesman for BAA is quoted as saying: "We were prepared to agree a price but this was upped to a level that was out of all reason.
Computer ram
"We are not prepared to be blackmailed and have, therefore, served writs on the appropriate defendants for passing off."
Bourke says the suggestion of blackmail is "ludicrous" and he is concentrating his efforts on his baa.net site while the legal action progresses.
There is no shortage of potential takers for sites with baa in the domain name.
For example, to name only a few: the British Aerobatic Association, the British Accounting Association, the Boston Athletics Association, Beer Across America and the British Ambulance Association.