Spectroscopic + photometric redshifts, stellar mass estimates, and rest-frame colors from the 3D-HST survey are combined with structural parameter measurements from CANDELS imaging to determine the galaxy size-mass distribution over the redshift range 0<z<3. Separating early- and late-type galaxies on the basis of star-formation activity, we confirm that early-type galaxies are on average smaller than late-type galaxies at all redshifts, and find a significantly different rate of average size evolution at fixed galaxy mass, with fast evolution for the early-type population, R_eff ~ (1+z)^-1.48, and moderate evolution for the late-type population, R_eff ~ (1+z)^-0.75. The large sample size and dynamic range in both galaxy mass and redshift, in combination with the high fidelity of our measurements due to the extensive use of spectroscopic data, not only fortify previous results, but also enable us to probe beyond simple average galaxy size measurements. At all redshifts the slope of the size-mass relation is shallow, R_eff ~ M_star^0.22, for late-type galaxies with stellar mass >3x10^9 M_sol, and steep, R_eff M_star^0.75, for early-type galaxies with stellar mass >2x10^10 M_sol. The intrinsic scatter is <~0.2 dex for all galaxy types and redshifts. For late-type galaxies, the logarithmic size distribution is not symmetric, but skewed toward small sizes: at all redshifts and masses a tail of small late-type galaxies exists that overlaps in size with the early-type galaxy population. The number density of massive (~10^11 M_sol), compact (R_eff < 2 kpc) early-type galaxies increases from z=3 to z=1.5-2 and then strongly decreases at later cosmic times.
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