We forecast the abilities of the Atacama Large Millimeter/submillimeter Array (ALMA) and the Square Kilometer Array (SKA) to detect CO and HI emission lines in galaxies at redshift z=3. A particular focus is set on Milky Way (MW) progenitors at z=3 for their detection within 24 h constitutes a key science goal of ALMA. The analysis relies on a semi-analytic model, which permits the construction of a MW progenitor sample by backtracking the cosmic history of all simulated present-day galaxies similar to the real MW. Results: (i) ALMA can best observe a MW at z=3 by looking at CO(3-2) emission. The probability of detecting a random model MW at 3-sigma in 24 h using 75 km/s channels is roughly 50%, and these odds can be increased by co-adding the CO(3-2) and CO(4-3) lines. These lines fall into ALMA band 3, which therefore represents the optimal choice towards MW detections at z=3. (ii) Higher CO transitions contained in the ALMA bands geq6 will be invisible, unless the considered MW progenitor coincidentally hosts a major starburst or an active black hole. (iii) The high-frequency array of SKA, fitted with 28.8 GHz receivers, would be a powerful instrument for observing CO(1-0) at z=3, able to detect nearly all simulated MWs in 24 h. (iv) HI detections in MWs at z=3 using the low-frequency array of SKA will be impossible in any reasonable observing time. (v) SKA will nonetheless be a supreme ha survey instrument through its enormous instantaneous field-of-view (FoV). A one year pointed HI survey with an assumed FoV of 410 sqdeg would reveal at least 10^5 galaxies at z=2.95-3.05. (vi) If the positions and redshifts of those galaxies are known from an optical/infrared spectroscopic survey, stacking allows the detection of HI at z=3 in less than 24 h.
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