A method of making a biocompatible component for reaction with a polyfunctional amine cross linker for the preparation of a medical adhesive composition, the method comprising the steps of: providing a multifunctional core compound, wherein the multifunctional core compound has from 3 to 12 functional groups and is either: (a) a polyol having molecular weight of from 130 to 20,000 g/mol and selected from the group consisting of polyether polyols, polyester polyols, branched chain ethoxylated alcohols, alkoxylated alcohols, polyvinyl alcohols, polyhydric alcohols, carboxylic acid esters of polyhydric alcohols, polyglycols, polylactone polyols, and combinations thereof, or (b) a multifunctional amine having molecular weight of from 132 to 10,000 g/mol; reacting the hydroxyl or amino groups of the multifunctional core compound with an aromatic, aliphatic or alicyclic diisocyanate thereby forming a multifunctional core possessing isocyanate-functionalized arms; followed by reacting the isocyanate groups of the isocyanate-functionalized arms with a polyalkylene oxide to attach polyalkyene oxide groups thereto, wherein the polyalkylene oxide is selected from the group consisting of polyethylene glycols, polypropylene glycols, polyethylene oxides, polypropylene oxides, polyethylene glycols with lactide linkages, polypropylene glycol-co-polyethylene oxide copolymers, polyethylene oxide/polypropylene oxide copolymers, and combinations thereof; followed by converting free hydroxyl groups at the ends of the polyalkylene oxide groups to terminal carboxylic groups by reacting them with an anhydride; and converting the terminal carboxylic groups to activated ester groups by reacting with N-hydroxysuccinimide or N-hydroxysulfosuccinimide, whereby the resulting biocompatible component has from 3 to 12 arms having said polyalkylene oxide groups functionalized with activated ester groups. providing a multifunctional core compound, wherein the multifunctional core compound has from 3 to 12 functional groups and is either: (a) a polyol having molecular weight of from 130 to 20,000 g/mol and selected from the group consisting of polyether polyols, polyester polyols, branched chain ethoxylated alcohols, alkoxylated alcohols, polyvinyl alcohols, polyhydric alcohols, carboxylic acid esters of polyhydric alcohols, polyglycols, polylactone polyols, and combinations thereof, or (b) a multifunctional amine having molecular weight of from 132 to 10,000 g/mol; reacting the hydroxyl or amino groups of the multifunctional core compound with an aromatic, aliphatic or alicyclic diisocyanate thereby forming a multifunctional core possessing isocyanate-functionalized arms; followed by reacting the isocyanate groups of the isocyanate-functionalized arms with a polyalkylene oxide to attach polyalkyene oxide groups thereto, wherein the polyalkylene oxide is selected from the group consisting of polyethylene glycols, polypropylene glycols, polyethylene oxides, polypropylene oxides, polyethylene glycols with lactide linkages, polypropylene glycol-co-polyethylene oxide copolymers, polyethylene oxide/polypropylene oxide copolymers, and combinations thereof; followed by converting free hydroxyl groups at the ends of the polyalkylene oxide groups to terminal carboxylic groups by reacting them with an anhydride; and converting the terminal carboxylic groups to activated ester groups by reacting with N-hydroxysuccinimide or N-hydroxysulfosuccinimide, whereby the resulting biocompatible component has from 3 to 12 arms having said polyalkylene oxide groups functionalized with activated ester groups.