A conjugate material which can be used as a coating for a medical device comprising a biocompatible and bioabsorbable copolymer having a comb-like structure. The copolymer comprises poly(vinyl alcohol) and a biodegradable polyester selected from a group consisting of polycaprolactone (PCL), poly-d,l-lactic acid (DL-PLA), poly-1-lactic acid (L-PLA), poly(glycolic acid) (PGA), poly(lactic acid-co-glycolic acid) (PLGA), poly(hydroxybutyrate), poly(hydroxybutyrate-co-valerate), polydioxanone, polyorthoester, polyanhydride, poly(glycolic acid-co-trimethylene carbonate), polyphosphoester, polyphosphoester urethane, poly (amino acids), poly(trimethylene carbonate), poly(iminocarbonate), polyalkylene oxalates, polyphosphazenes, and aliphatic polycarbonates, and poly(ether-co-ester). Substantially all side chains of the copolymer are conjugated to a heparin anti-thrombotic agent.