We resolve the host galaxies of seven gravitationally lensed quasars at redshift 1.5 to 2.8 using observations with the Atacama Large (sub-)Millimetre Array. Using a visibility-plane lens modelling technique, we create pixellated reconstructions of the dust morphology, and CO line morphology and kinematics. We find that the quasar hosts in our sample can be distinguished into two types: 1) galaxies characterised by clumpy, extended dust distributions ($R_{rm eff}sim2$ kpc) and mean star formation rate surface densities comparable to sub-mm-selected dusty star-forming galaxies ($Sigma_{rm SFR}sim3$ M$_{odot}$ yr$^{-1}$ kpc$^{-2}$); 2) galaxies that have sizes in dust emission similar to coeval passive galaxies and compact starbursts ($R_{rm eff}sim0.5$ kpc), with high mean star formation rate surface densities ($Sigma_{rm SFR}=$ 400$-$4500 M$_{odot}$ yr$^{-1}$ kpc$^{-2}$) that may be Eddington-limited or super-Eddington. The small size of some quasar hosts suggests that we observe them at a stage in their transformation into compact spheroids, where a high density of dynamically unstable gas leads to efficient star formation and black hole accretion. For the one system where we probe the mass of the gas reservoir, we find a gas fraction of just $0.06 pm 0.04$ and a depletion timescale of $50 pm 40$ Myr, suggesting it is transitioning into quiescence. In general, we expect that the extreme level of star formation in the compact quasar host galaxies will rapidly exhaust their gas reservoirs and could quench with or without help from active galactic nuclei feedback.
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