When the 23-year-old was growing up in Regina, it was the sweater he saw most often on his television. And it ended up becoming a symbol he started to identify with what it meant to play in the NHL.
"You grow up, you watch 'Hockey Night in Canada' and the team you watch is the Toronto Maple Leafs," Bozak said Saturday morning. "You go out in your backyard, you play hockey and you pretend to be guys on that team. It's just been a dream to play for them."
Maple Leafs GM Brian Burke presented Bozak with one of the team's blue home jerseys one day after signing the centre to a two-year, entry-level contract.
There were as many as 25 NHL teams that were interested in his services and it took roughly a week for him to make a final decision. The Leafs were able to offer him more than just the chance to play for an Original Six team.
"Tyler's being polite - part of the reason he signed here is because he sees opportunity as well," said Burke.
He won't get a chance to play a game at Air Canada Centre until next season. Bozak missed a significant portion of his sophomore year with the University of Denver because of an injury to his left knee and should be ready to skate with the Leafs at the team's prospect camp over the summer.
The injury itself isn't something he's concerned with. Bozak actually returned for the last game of Denver's season and had a goal and an assist during a 4-2 loss to Miami of Ohio last weekend.
"I feel really good," said Bozak. "I'm going to see the medical staff here and the doctors and they're going to help me determine when I'm ready to go."
The arrival of Bozak and fellow college free agent Christian Hanson has provided some optimism for fans in Toronto. They were among the most coveted guys available from the U.S. college hockey ranks.
While neither is seen as a lock to become an impact player, the Leafs are optimistic that both have the potential to become top-six forwards. And it could happen as soon as next season.
When asked about when Bozak might be ready for the NHL, Burke indicated that the onus was on the player.
"It's up to Tyler," he said. "We're betting on this young man, we think he's going to play. He's got to get stronger, a little bit bigger...
"When he plays here is up to him. But we think he's going to get there. We have high hopes for this young man."
A chance is the biggest thing he's been looking for.
Bozak left home as a teenager and spent three seasons playing for Victoria in the BCHL. He was the league's scoring leader in 2006-07, putting up 45 goals and 128 points in 59 games.
However, his small stature at the time kept him from getting drafted by an NHL team.
"I was always a smaller guy growing up," said Bozak. "So (that was) kind of looked (down) upon. I just worked hard and had great coaches and great development my whole way up. That's what got me here now."
He's currently listed at six foot one, 180 pounds.
Bozak described the last week as being the most exciting of his life. Once Denver was eliminated from the NCAA tournament, he flew to Toronto and spent time going through NHL offers with his agent at Newport Sports Management.
Even though he was drawn to the history of the Leafs, he wasn't a fan of any particular NHL team as a kid.
"I was just a hockey fan growing up," said Bozak. "Regina, Saskatchewan - we haven't got much. I like the Saskatchewan Roughriders a lot.
"Just grew up watching hockey and playing in the backyard rink."
He's got a favourite team now.
Burke was quite candid in saying that he hopes Toronto isn't a destination for U.S. college free agents in the future because that will mean the team is too good to provide those players an opportunity. In the meantime, he plans to try and stockpile as much talent as he can.
"I could care less where players come from," said Burke. "We intend to build this team with junior players, college players, European players. If they start playing hockey on Mars, we'll draft players from Mars.
"I could give a rat's ass where a player comes from as long as he can play here."