Context : Direct imaging has led to the discovery of several giant planet and brown dwarf companions .
These imaged companions populate a mass , separation and age domain ( mass > 1 ~ { } M _ { \mathrm { Jup } } , orbits > 5 AU , age < 1 Gyr ) quite distinct from the one occupied by exoplanets discovered by the radial velocity or transit methods .
This distinction could pinpoint that different formation mechanisms are at play .

Aims : We aim at investigating correlations between the host star ’ s mass and the presence of wide-orbit giant planets , and at providing new observational constraints on planetary formation models .

Methods : We observed 58 young and nearby M-type dwarfs in L ^ { \prime } -band with the VLT/NaCo instrument and used ADI algorithms to optimize the sensitivity to planetary-mass companions and to derive the best detection limits .
We estimate the probability of detecting a planet as a function of its mass and physical separation around each target .
We conduct a Bayesian analysis to determine the frequency of substellar companions orbiting low-mass stars , using a homogenous sub-sample of 54 stars .

Results : We derive a frequency of 4.4 ^ { +3.2 } _ { -1.3 } \% for companions with masses in the range of 2-80 M _ { \mathrm { Jup } } , and 2.3 ^ { +2.9 } _ { -0.7 } % for planetary mass companions ( 2-14 M _ { \mathrm { Jup } } ) , at physical separations of 8 to 400 AU for both cases .
Comparing our results with a previous survey targeting more massive stars , we find evidence that substellar companions more massive than 1 M _ { \mathrm { Jup } } with a low mass ratio Q with respect to their host star ( Q < 1 % ) , are less frequent around low-mass stars .
This may represent an observational evidence that the frequency of imaged wide-orbit substellar companions is correlated with stellar mass , corroborating theoretical expectations .
On the opposite , we show statistical evidence that intermediate-mass ratio ( 1 % < Q < 5 % ) companion with masses > 2 M _ { \mathrm { Jup } } might be independent from the mass of the host star .

Conclusions :