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tokens: We gratefully acknowledge the ALMA, IRAM, CARMA, and MOPRA facilities and thank the M33 and MAGMA teams for making their data public. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.00876.S, ADS/JAO.ALMA#2012.00650. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Based on observations carried out with the IRAM 30 m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). A.E. acknowledges partial support from grants PFB #06, FONDECYT #1130458, and ACT #1101. A.H. acknowledges support from the Centre National d’Etudes Spatiales (CNES). A.U. acknowledges support from Spanish MINECO grants AYA2012-32295 and FIS2012-32096. J.M.D.K. gratefully acknowledges financial support in the form of a Gliese Fellowship and an Emmy Noether Research Group from the Deutsche Forschungsgemeinschaft (DFG), grant number KR4801/1-1. J.P. thanks the CNRS/INSU program PCMI for support. M.Q. and S.E.M. acknowledge funding from the Deutsche Forschungsgemeinschaft (DFG) via grants SCHI 536/7-2, SCHI 536/5-1, and SCHI 536/7-1 as part of the priority program SPP 1573 “ISM-SPP: Physics of the Interstellar Medium.” M.Q., S.E.M., and E.S. acknowledge financial support to the DAGAL network from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement number PITN-GA-2011-289313. E.R. is supported by a Discovery Grant from NSERC of Canada. G.B. is supported by CONICYT/FONDECYT, Programa de Iniciacion, Folio 11150220.