We explore heavy-element nucleosynthesis by rapid neutron capture ( r-process ) in the decompressing ejecta from the surface of a neutron star . The decompression is triggered by a violent phase transition to strange quark matter ( quark-nova scenario ) . The presence of neutron-rich large Z nuclei ( 40 , 95 ) < ( Z,A ) < ( 70 , 177 ) , the large neutron-to-seed ratio , and the low electron fraction Y _ { e } \sim 0.03 in the decompressing ejecta present favorable conditions for the r-process . We perform network calculations that are adapted to the quark-nova conditions , and which mimic usual ( n - \gamma ) equilibrium r-process calculations during the initially cold decompression phase . They match to dynamical r-process calculations at densities below neutron drip ( 4 \times 10 ^ { 11 } g cm ^ { -3 } ) . We present results for the final element abundance distribution with and without heating from nuclear reactions , and compare to the solar abundance pattern of r-process elements . We highlight the distinguishing features of quark-novae by contrasting it with conventional nucleosynthetic sites such as type II supernovae and neutron star mergers , especially in the context of heavy-element compositions of extremely metal-deficient stars .