Context : Ultra-cool dwarfs of the L spectral type ( T _ { eff } = 1400 –2200 K ) are known to have dusty atmospheres .
Asymmetries of the dwarf surface may arise from rotationally-induced flattening and dust-cloud coverage , and may result in non-zero linear polarisation through dust scattering .

Aims : We aim to study the heterogeneity of ultra-cool dwarfs ’ atmospheres and the grain-size effects on the polarisation degree in a sample of nine late M , L and early T dwarfs .

Methods : We obtain linear polarimetric imaging measurements using FORS1 at the Very Large Telescope , in the Bessel I filter , and for a subset in the Bessel R and the Gunn z filters .

Results : We measure a polarisation degree of ( 0.31 \pm 0.06 ) % for LHS102BC .
We fail to detect linear polarisation in the rest of our sample , with upper-limits on the polarisation degree of each object of 0.09 % to 0.76 % ( 95 % of confidence level ) , depending on the targets and the bands .
For those targets we do not find evidence of large-scale cloud horizontal structure in our data .
Together with previous surveys , our results set the fraction of ultra-cool dwarfs with detected linear polarisation to 30 ^ { +10 } _ { -6 } % ( 1- \sigma errors ) .
From the whole sample of well-measured objects with errors smaller than 0.1 % , the fraction of ultra-cool dwarfs with polarisation degree larger than 0.3 % is smaller than 16 % ( 95 % confidence level ) .

Conclusions : For three brown dwarfs , our observations indicate polarisation degrees different ( at the 3- \sigma level ) than previously reported , giving hints of possible variations .
Our results fail to correlate with the current model predictions for ultra-cool dwarf polarisation for a flattening-induced polarisation , or with the variability studies for a polarisation induced by an heterogeneous cloud cover .
This stresses the intricacy of each of those tasks , but may as well proceed from complex and dynamic atmospheric processes .