ABSTRACT This paper presents maps of the J=2-1 transition of CO towards the Draco nebula intermediate-velocity cloud (IVC). The maps cover 8500 square arcmin with a velocity resolution of 0.33 km s$^{-1}$ and angular resolution of 38 ${\rm arcsec}$, or 0.11 pc at the cloud distance of 600 pc. The mapped area includes all the emission detected by the Herschel satellite with 250 $\mu$m intensity >5 MJy sr−1. Previously published observations of the far-infrared (far-IR) emission and the 21 cm line of HI are used to derive the column density distribution of H$_2$ and the abundance ratio CO/H$_2$, as well as the distribution of the molecular fraction of hydrogen, which approaches 90 per cent over much of the brighter parts of the nebula. The CO emission is highly clumpy and closely resembles the structures seen in far-IR images. The kinematics of the CO show supersonic motions between clumps but near-thermal to trans-sonic motions within clumps, consistent with model predictions that the scale length for dissipation of supersonic turbulence should be $\sim 0.1$ pc, mediated by kinematic viscosity and/or ambipolar diffusion. Different parts of the nebula show evidence for a spread of molecular formation time-scales of a few 10$^5$ yr, comparable with the dynamical time-scale of the infalling gas. The IVC will likely merge with the Galactic interstellar medium in $\sim 10^7$ yr, and the densest clumps may form an unbound cluster of low-mass stars.