  We investigate the star-forming main sequence of the host galaxies of a
large, well-defined sample of 453 redshift $\sim$0.3 quasars with previously
available star formation rates by deriving stellar masses from modeling their
broad-band ($grizy$) spectral energy distribution. We perform two-dimensional,
simultaneous, multi-filter decomposition of Pan-STARRS1 3$\pi$ Steradian Survey
images to disentangle the active galactic nucleus (AGN) from its host galaxy,
by explicitly considering, for the first time, the wavelength variation of
galaxy structures. We quantify the S\'ersic profiles and sizes of the host
galaxies from mock AGNs generated from both real and idealized galaxies.
Detailed morphological classifications of the calibration galaxy sample with
Hubble Space Telescope images enable us to estimate crude morphological types
of the quasars. Although the majority ($\sim$60%) of the quasars are hosted by
bulge-dominated, early-type galaxies, a substantial fraction ($\sim$40%) reside
in disk-dominated, late-type galaxies, suggesting that at least in these
systems major mergers have not played a significant role in regulating their
AGN activity, in agreement with recent simulations and observations of nearby
quasars. The vast majority ($\sim$90%) of the quasars have star formation rates
that place them on or above the galaxy star-forming main sequence, with more
rapidly accreting AGNs displaced further above the main sequence. Quasar host
galaxies generally follow the stellar mass-size relation defined by inactive
galaxies, both for late-type and early-type systems, but roughly 1/3 of the
population has smaller sizes at a given stellar mass, reminiscent of compact
star-forming galaxies at higher redshift.
