Context : The asymptotic giant branch ( AGB ) marks the final evolutionary stage of stars with initial masses between \sim 0.8 and 8 M _ { \odot } .
During this phase , stars undergo copious mass loss .
The well-accepted mass-loss mechanism requires radiation pressure acting on dust grains that form in the density-enhanced and extended AGB stellar atmospheres .
The details of the mass-loss process are not yet well understood , however .

Aims : We aim to study the spatial distribution and properties of the first grains that form around AGB stars .

Methods : Using the extreme-adaptive-optics imager and polarimeter SPHERE/ZIMPOL , we observed light polarised by grains around the AGB stars W Hya , SW Vir , and R Crt , with mass-loss rates between 10 ^ { -7 } and 10 ^ { -6 } ~ { } M _ { \odot } ~ { } { yr ^ { -1 } } .

Results : We find the distribution of dust to be asymmetric around the three targets .
A biconical morphology is seen for R Crt , with a position angle that is very similar to those inferred from interferometric observations of maser emission and of mid-infrared continuum emission .
The cause of the biconical outflow can not be directly inferred from the ZIMPOL data .
The dust grains polarise light more efficiently at 0.65 \mu m for R Crt and SW Vir and at 0.82 \mu m for W Hya .
This indicates that at the time of the observations , the grains around SW Vir and R Crt had sizes < 0.1 ~ { } \mu m , while those around W Hya were larger , with sizes \gtrsim 0.1 ~ { } \mu m. The asymmetric distribution of dust around R Crt makes the interpretation more uncertain for this star , however .
We find that polarised light is produced already from within the visible photosphere of W Hya , which we reproduce using models with an inner dust shell that is optically thick to scattering .
The radial profile of the polarised light observed around W Hya reveal a steep dust density profile .
We find the wind-acceleration region of W Hya to extend to at least \sim 7 ~ { } R _ { \star } , in agreement with theoretical predictions of wind acceleration up to \sim 12 ~ { } R _ { \star } .

Conclusions :