Zabransky came to North America for the 1996-97 season and got an extended look with the Blues. In 34 games he scored a goal (in a game vs New Jersey) and five assists while earning 44 penalty minutes. For a big man he could get around the ice pretty well and made safe decisions to get the puck out of his zone. His seemed more comfortable once coach Mike Keenan was replaced.
Ultimately the Blues found other defensemen that offered a little more with the puck. Zabransky was farmed out for most of the 1997-98 season. And when Zabransky failed to make the Blues roster out of training camp for the 1998-99 season he was allowed to return Europe rather report back to the minor leagues.
Zabransky would play six seasons in his native Czech Republic, but he had to retire prematurely due to health problems. He had battled severe groin problems while still trying to play, missing many games.
Zabransky would save the bankrupt HC Kometa Brno hockey team by becoming it's owner. He would handle many duties in the hockey department, including coach.