One of the key goals of the BLUEDISK survey is to characterize the impact of gas accretion in disc galaxies in the context of galaxy evolution. It contains 50 disc galaxies in the stellar mass range 10(10)-10(11)M(circle dot), of which half are bluer and more HI-rich galaxies than their HI-normal (control) counterparts. In this paper, we investigate how ongoing disc growth affects the molecular gas distribution and the star formation efficiency in these galaxies. We present (CO)-C-12 observations from the IRAM 30-m telescope in 26 galaxies of the BLUEDISK survey. We compare the amount and spatial distribution of the molecular gas to key quantities such as atomic gas, stellar mass and surface density, star formation rate (SFR) and metallicity. We analyse the SFR per unit gas (SFR/H I and SFR/H-2) and relate all those parameters to general galaxy properties (HI-rich/control disc, morphology, etc.). We find that the HI-rich galaxies have similar H-2 masses as the control galaxies. In their centres, HI-rich galaxies have lower H-2/H I ratios and marginally shorter molecular gas depletion times. However, the main differences between the two samples occur in the outer parts of the discs, with the HI-rich galaxies having slightly smaller CO discs (relative to the optical radius R-25) and steeper CO and metallicity gradients than the control galaxies. The ongoing accretion of HI at large radii has thus not led to an appreciable growth of the CO discs in our sample. Based on depletion times, we estimate that this gas will contribute to star formation on time-scales of at least 5 Gyr. © 2016 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. © 2016 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

We are grateful to Mei-Ling Huang for her help with the Bluedisk SFR data. We would like to thank Barbara Catinella and Sacha Hony for careful reading of the manuscript and helpful comments, as well as David Elbaz and Adam Leroy for interesting discussions. We also thank the referee for a very constructive report. DC and FB acknowledge support from DFG grant BI 1546/1-1. JP acknowledges support from the CNRS program ‘Physique et Chimie du Milieu Interstellaire’ (PCMI). JMvdH acknowledges support from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement nr. 291531. This work is based on observations carried out with the IRAM 30-m Telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). This publication makes use of data products from the WISE, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration.