Context : The existence of dusty debris disks around a large fraction of solar type main-sequence stars , inferred from excess far-IR and submillimetre emission compared to that expected from stellar photospheres , suggests that leftover planetesimal belts analogous to the asteroid- and comet reservoirs of the Solar System are common . Aims : In order to detect and characterise cold extended dust originating from collisions of small bodies in disks , belts , or rings at Kuiper-Belt distances ( 30–50 AU or beyond ) sensitive submillimetre observations are essential . Measurements of the flux densities at these wavelengths will extend existing IR photometry and permit more detailed modelling of the Rayleigh-Jeans tail of the disks spectral energy distribution ( SED ) , effectively constraining dust properties and disk extensions . By observing stars spanning from a few up to several hundred Myr , the evolution of debris disks during crucial phases of planet formation can be studied . Methods : We have performed 870 \mu m observations of 22 exo-Kuiper-Belt candidates , as part of a Large Programme with the LABOCA bolometer at the APEX telescope . Dust masses ( or upper limits ) were calculated from integrated 870 \mu m fluxes , and fits to the SED of detected sources revealed the fractional dust luminosities f _ { \mathrm { dust } } , dust temperatures T _ { \mathrm { dust } } , and power-law exponents \beta of the opacity law . Results : A total of 10 detections with at least 3 \sigma significance were made , out of which five ( HD 95086 , HD 131835 , HD 161868 , HD 170773 , and HD 207129 ) have previously never been detected at submillimetre wavelengths . Three additional sources are marginally detected with > 2.5 \sigma significance . The best-fit \beta parameters all lie between 0.1 and 0.8 , in agreement with previous results indicating the presence of grains that are significantly larger than those in the ISM . From our relatively small sample we estimate f _ { \mathrm { dust } } \propto t ^ { - \alpha } , with \alpha \sim 0.8–2.0 , and identify an evolution of the characteristic radial dust distance R _ { \mathrm { dust } } that is consistent with the t ^ { 1 / 3 } increase predicted from models of self-stirred collisions in debris disks . Conclusions :