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We present the first interferometric blind HI survey of the Fornax galaxycluster, which covers an area of 15 deg$^2$ out to the cluster $R_{vir}$. Thesurvey has a resolution of 67''x95'' and 6.6 km$s^{-1}$ with a 3$\sigma$sensitivity of N(HI)~2x10$^{19}$ cm$^{-2}$ and MHI 2x10$^7$ M$_\odot$.  We detect 16 galaxies out of 200 spectroscopically confirmed Fornax clustermembers. The detections cover ~3 orders of magnitude in HI mass, from 8x10$^6$to 1.5x10$^{10}$ M$_\odot$. They avoid the central, virialised region of thecluster both on the sky and in projected phase-space, showing that they arerecent arrivals and that, in Fornax, HI is lost within a crossing time, ~2 Gyr.Half of these galaxies exhibit a disturbed HI morphology, including severalcases of asymmetries, tails, offsets between HI and optical centres, and a caseof a truncated HI disc suggesting that they have been interacting within or ontheir way to Fornax. Our HI detections are HI-poorer and form stars at a lowerrate than non-cluster galaxies in the same $M_\star$ range. Low mass galaxiesare more strongly affected throughout their infall towards the cluster. TheMHI/$M_\star$ ratio of Fornax galaxies is comparable to that in the Virgocluster. At fixed $M_\star$, our HI detections follow the non-cluster relationbetween MHI and the star formation rate, and we argue that this implies that sofar they have lost their HI on a timescale $\gtrsim$1-2 Gyr. Deeper inside thecluster HI removal is likely to proceed faster, as confirmed by a population ofHI-undetected but H$_2$-detected star-forming galaxies. Based on ALMA data, wefind a large scatter in H$_2$-to-HI mass ratio, with several galaxies showingan unusually high ratio that is probably caused by faster HI removal.  We identify an HI-rich subgroup of possible interacting galaxies dominated byNGC 1365, where pre-processing is likey to have taken place.

A blind ATCA HI survey of the Fornax galaxy cluster: properties of the HI detections