We suggest that a high proportion of brown dwarf stars are formed by gravitational fragmentation of massive extended discs around Sun-like primary stars .
We argue that such discs should arise frequently , but should be observed infrequently , precisely because they fragment rapidly .
By performing an ensemble of radiation-hydrodynamic simulations , we show that such discs typically fragment within a few thousand years , and produce mainly brown dwarf ( BD ) stars , but also planetary-mass ( PM ) stars and very low-mass hydrogen-burning ( HB ) stars .
Subsequently most of the lower-mass stars ( i.e .
the PM and BD stars ) are ejected by mutual interactions .
We analyse the statistical properties of these stars , and compare them with observations .

After a few hundred thousand years the Sun-like primary is typically left with a close low-mass HB companion , and two much wider companions : a low-mass HB star and a BD star , or a BD-BD binary .
The orbits of these companions are highly eccentric , and not necessarily coplanar , either with one another , or with the original disc .
There is a BD desert extending out to at least \sim 100 { AU } ; this is because BDs tend to be formed further out than low-mass HB stars , and then they tend to be scattered even further out , or even into the field .

BDs form with discs of a few Jupiter masses and radii of a few tens of AU , and they are more likely to retain these discs if they remain bound to the primary star .
Binaries form by pairing of the newly-formed stars in the disc , giving a low-mass binary fraction of \sim 0.16 .
These binaries include close and wide BD/BD binaries and BD/PM binaries .
Binaries can be ejected into the field and survive , even if they have quite wide separations .
BDs that remain as companions to Sun-like stars are more likely to be in BD/BD binaries than are BDs ejected into the field .
The presence of close and distant companions around Sun-like stars may inhibit planet formation by core accretion .

We conclude that disc fragmentation is a robust mechanism for BD formation .
Even if only a small fraction of Sun-like stars host the required massive extended discs , this mechanism can produce all the PM stars observed , most of the BD stars , and a significant proportion of the very low-mass HB stars .