GRBs generate an afterglow emission that can be detected from radio to X-rays during days, or even weeks after the initial explosion. The peak of this emission crosses the mm/submm range during the first hours to days, making their study in this range crucial for constraining the models. Observations have been limited until now due to the low sensitivity of the observatories in this range. We present observations of 10 GRB afterglows obtained from APEX and SMA, as well as the first detection of a GRB with ALMA, and put them into context with all the observations that have been published until now in the spectral range that will be covered by ALMA. The catalogue of mm/submm observations collected here is the largest to date and is composed of 102 GRBs, of which 88 had afterglow observations, whereas the rest are host galaxy searches. With our programmes, we contributed with data of 11 GRBs and the discovery of 2 submm counterparts. In total, the full sample, including data from the literature, has 22 afterglow detections with redshift ranging from 0.168 to 8.2. GRBs have been detected in mm/submm wavelengths with peak luminosities spanning 2.5 orders of magnitude, the most luminous reaching 10^33erg s^-1 Hz^-1. We observe a correlation between the X-ray brightness at 0.5 days and the mm/submm peak brightness. Finally we give a rough estimate of the distribution of peak flux densities of GRB afterglows, based on the current mm/submm sample. Observations in the mm/submm bands have been shown to be crucial for our understanding of the physics of GRBs, but have until now been limited by the sensitivity of the observatories. With the start of the operations at ALMA, the sensitivity will be increased by more than an order of magnitude. Our estimates predict that, once completed, ALMA will detect up to 98% of the afterglows if observed during the passage of the peak synchrotron emission.
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