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(abridged) We explore how ALMA observations can probe high-redshift galaxiesin unprecedented detail. We discuss the main observables that are excited bythe large-scale starburst, and formulate expectations for the chemistry and thefluxes in the center of active galaxies, where chemistry may be driven by theabsorption of X-ray photons. We show that such X-ray dominated regions (XDRs)should be large enough to be resolved with ALMA, and predict the expectedamount of emission in CO and various fine-structure lines. We discuss how suchXDRs can be distinguished from a strong starburst on the same spatial scalesbased on the CO line SED. Our models are compared to known sources like NGC1068 and APM 08279. We also analyze the properties of the z=6.42 quasar SDSSJ114816.64+525150.3, and find that the observed emission in CO, [CII] and [CI]requires a dense warm and a low-density cold gas component. We estimate theexpected number of sources at redshifts higher than 6, finding that one couldexpect one black hole with $10^6$ solar masses per arcmin$^2$.

Probing high-redshift quasars with ALMA. I. Expected observables and potential number of sources