While all models for the evolution of galaxies require the accretion of gasto sustain their growth via on-going star formation, it has proven difficult todirectly detect this inflowing material. In this paper we use data of nearbystar-forming galaxies in the SDSS IV Mapping Nearby Galaxies at Apache PointObservatory (MaNGA) survey to search for evidence of accretion imprinted in thechemical composition of the interstellar medium. We measure both the O/H andN/O abundance ratios in regions previously identified as having anomalously lowvalues of O/H. We show that the unusual locations of these regions in the N/Ovs. O/H plane indicate that they have been created through the mixing of diskgas having higher metallicity with accreted gas having lower metallicity. Takentogether with previous analysis on these anomalously low-metallicity regions,these results imply that accretion of metal-poor gas can probably sustain starformation in present-day late-type galaxies.

We compile observations of molecular gas contents and infrared-based starformation rates (SFRs) for 112 circumnuclear star forming regions, in order tore-investigate the form of the disk-averaged Schmidt surface density starformation law in starbursts. We then combine these results with total gas andSFR surface densities for 153 nearby non-starbursting disk galaxies from de losReyes \& Kennicutt (2019), to investigate the properties of the combined starformation law, following Kennicutt (1998; K98). We confirm that the combinedSchmidt law can be fitted with a single power law with slope $n = 1.5\pm0.05$(including fitting method uncertainties), somewhat steeper than the value $n =1.4\pm0.15$ found by K98. Fitting separate power laws to the non-starburstingand starburst galaxies, however, produces very different slopes ($n =1.34\pm0.07$ and $0.98\pm0.07$, respectively), with a pronounced offset in thezeropoint ($\sim$0.6\,dex) of the starburst relation to higher SFR surfacedensities. This offset is seen even when a common conversion factor between COintensity and molecular hydrogen surface density is applied, and is confirmedwhen disk surface densities of interstellar dust are used as proxies for gasmeasurements. Tests for possible systematic biases in the starburst data failto uncover any spurious sources for such a large offset. We tentativelyconclude that the global Schmidt law in galaxies, at least as it isconventionally measured, is bimodal or possibly multi-modal. Possible causesmay include changes in the small-scale structure of the molecular ISM or thestellar initial mass function. A single $n \sim 1.5$ power law still remains asa credible approximation or "recipe" for analytical or numerical models ofgalaxy formation and evolution.

Using a sample of ~15,000 kpc-scale star-forming spaxels in 28 galaxies drawnfrom the ALMA-MaNGA QUEnching and STar formation (ALMaQUEST) survey, weinvestigate the galaxy-to-galaxy variation of the `resolved' Schmidt-Kennicuttrelation (rSK; Sigma_H2 - Sigma_SFR), the `resolved' star forming main sequence(rSFMS; Sigma_* - Sigma_SFR) and the `resolved' molecular gas main sequence(rMGMS; Sigma_* - Sigma_H2). The rSK relation, rSFMS and rMGMS all showsignificant galaxy-to-galaxy variation in both shape and normalization,indicating that none of these relations is universal between galaxies. TherSFMS shows the largest galaxy-to-galaxy variation and the rMGMS the least. Bydefining an `offset' from the average relations, we compute a Delta_rSK,Delta_rSFMS, Delta_rMGMS for each galaxy, to investigate correlations withglobal properties. We find the following correlations with at least 2 sigmasignificance: the rSK is lower (i.e. lower star formation efficiency) ingalaxies with higher M_*, larger Sersic index and lower specific SFR (sSFR);the rSFMS is lower (i.e. lower sSFR) in galaxies with higher M_* and largerSersic index; the rMGMS is lower (i.e. lower gas fraction) in galaxies withlower sSFR. In the ensemble of all 15,000 data points, the rSK relation andrMGMS show equally tight scatters and strong correlation coefficients, comparedwith a larger scatter and weaker correlation in the rSFMS. Moreover, whilstthere is no correlation between Delta_rSK and Delta_rMGMS in the sample, theoffset of a galaxy's rSFMS does correlate with both of the other two offsets.Our results therefore indicate that the rSK and rMGMS are independentrelations, whereas the rSFMS is a result of their combination.

In order to investigate the role of gas in the demise of star formation onkpc-scales, we compare the resolved molecular gas main sequence (rMGMS: Sigma_*vs Sigma_H2) of star-forming regions to the sequence of `retired' regions thathave ceased to form new stars. Using data from the ALMaQUEST survey, we findthat retired spaxels form a rMGMS that is distinct from that of star-formingspaxels, offset to lower Sigma_H2 at fixed Sigma_* by a factor of ~5. We studythe rMGMS of star-forming and retired spaxels on a galaxy-by-galaxy basis foreight individual ALMaQUEST galaxies. Six of these galaxies have their retiredspaxels concentrated within the central few kpc. Molecular gas is detected in40-100% of retired spaxels in the eight galaxies in our sample. Both thestar-forming and retired rMGMS show a diversity in normalization fromgalaxy-to-galaxy. However, in any given galaxy, the rMGMS for retired regionsis found to be distinct from the star-forming sequence and gas fractions ofretired spaxels are up to an order of magnitude lower than the star-formingspaxels. We conclude that quenching is associated with a depletion (but notabsence) of molecular gas via a mechanism that typically begins in the centreof the galaxy.