From 1958 to his death in 1992, Bacon exclusively used Marlborough Fine Art to show his work.
But his estate is alleging "undue influence" and breach of duty in a claim which could be worth £100m.
The defendants, who's headquarters are in Liechtenstein, are contesting the allegations as "unfounded".
The value of Bacon's work can be gauged by the sale of three paintings of his long-time partner John Edwards which sold for £3m.
Geoffrey Vos QC, representing the estate, told Mr Justice Patten that Marlborough UK director Valerie Beston "organised much if not all of Francis Bacon's professional and personal life.
"One of her principal roles on behalf of Marlborough UK was the removal of the paintings that he completed to its own gallery as soon as the paint was dry - in Marlborough's own words 'in Bacon's best interests'."
'Fair'
Bacon's estate is alleging that, subject to a fair allowance for the work it did, Marlborough should not have been keeping up to 70% of the value of Bacon's paintings.
The estate believes a fair amount would be a third of the total value.
It wants to see "proper accounting from Marlborough, so as to be able to establish that there was a fair balance struck between the interests of the gallery and Bacon."
Mr Justice Patten was listening to the outline of the arguments to decide on a timetable for the case which is scheduled for January 2002.