Career
He is currently playing in the Austrian Hockey League (EBEL) with the EHC Black Wings Linz. Kozek was drafted 53rd overall by the Atlanta Thrashers in the 2005 National Hockey League Entry Draft. Kozek played collegiately at the University of North Dakota from 2005 to 2009.
He helped UND capture the WCHA championship in 2006, followed by a trip to the National Collegiate Athletic Association Frozen Four, where the Fighting Hawks were defeated by Boston College.
In 2007, UND again made it to the National Collegiate Athletic Association Frozen Four and again fells short in the semifinal against Boston College. Kozek reached a third National Collegiate Athletic Association Frozen Four with North Dakota in 2008, but for the third consecutive year the Fighting Hawks did not get passed British Columbia in the semis.
Kozek was named to the WCHA All-Academic Team his junior year. After his National Collegiate Athletic Association career, Kozek played for the Chicago Wolves in the American Hockey League, seeing action in five games of the 2008-2009 season.
He then signed a deal with the Atlanta Thrashers and was assigned to their affiliate, the Chicago Wolves, where he made 126 AHL appearances.
On March 7, 2011, Kozek was sent by the Thrashers on loan to the Hershey Bears, affiliate of the Washington Capitals, in exchange for Capitals prospect Josh Godfrey. In the following season, Kozek embarked on his career abroad, first agreeing to a one-year stint in the Asia League Ice Hockey with the Nikko Ice Buckinghamshire. He then moved to the more competitive Austrian top-flight EBEL with Dornbirner European Commission for the 2012-2013 campaign.
He led the league in goalscoring that season, chipping in with 38 goals (plus 20 assists) in 54 games.
After one year at Dornbirn, Kozek moved to EBEL rivals EHC Linz prior to the 2013-2014 season.