Former NFL wide receiver Randy Moss, right, poses with a...

Former NFL wide receiver Randy Moss, right, poses with a bust of himself and with his presenter, son Thaddeus Moss, during inductions at the Pro Football Hall of Fame, Saturday, Aug. 4, 2018 in Canton, Ohio. Credit: AP/Gene J. Puskar

Most of the tight ends and receivers who are about to be drafted probably have entertained the thought of catching an NFL touchdown pass thrown by Tom Brady. He’s the greatest quarterback of all time, and at 42, there’s no telling how much longer he’ll be around to dole out the scoring passes.

Being a young player in the league and having the chance to be part of such history, well, that would be something to tell your kids about.

Or, if you are Thaddeus Moss, compare notes on it with your dad.

Moss, a tight end from LSU in the upcoming draft, is the son of former NFL wide receiver and Pro Football Hall of Famer Randy Moss. He has plenty of memories of growing up around the game and those who played it at the highest level.

“I was in the [Patriots'] facility once or twice before,” he said. “Meeting Tom Brady when I was younger, I was sitting there star-struck. Walking down the hallway, seeing Tedy Bruschi, seeing [Mike] Vrabel when I was younger, those were probably the fondest memories that I have.”

Soon, Moss may have a chance to not only meet NFL stars but play alongside them — or even be one. He had  surgery to repair a foot injury that was discovered at the NFL Scouting Combine in February, which could hurt his draft status, but Moss’ talent — and pedigree — virtually ensure that a team will take a chance on him.

It might even be the Bucs, Brady’s new team.

“It would mean a lot,” Moss said of possibly following his father as one of Brady’s targets. “Just to catch a touchdown pass period in the NFL would mean a lot. To catch it from Tom Brady knowing that he threw a good amount of touchdown passes to my father? It would be a good story.”

Moss is one of a handful of second-generation players who will be entering the league this offseason, carrying on the family name — and in some cases the first name as well — while having the opportunity to expand that legacy.

Antoine Winfield Jr. is a cornerback from the University of Minnesota. His father, Antoine, played for 14 NFL seasons and was a three-time Pro Bowler despite being somewhat undersized at 5-9 and 185 pounds.

“It’s just incredible to see what he did at his size,” Antoine Jr. said. “He comes home every day and I see him, he’s a little guy. But the next thing you know, I see him on TV and he’s out there ballin’ with great players. That is what was really incredible about watching him play.”

Junior isn’t much bigger, at 5-9 and about 200 pounds.

“We’re almost about the same in size,” he said. “My dad had a lot of heart, and that’s kind of what I looked up to in him. Seeing him go out there against professionals and great guys that you see on TV all the time, that’s something I kind of [model] my game after. It’s not about how big you are, how tall you are, it’s about how much fight you have.”

Size does matter at some positions, though, and having NFL offensive lineman Jon Runyan for a father gave Jon Runyan Jr. the genetic push to be a 6-4, 306-pound prospect from Michigan (his father played there, too). It wasn’t always easy being Jon’s son, though.

“Growing up, it was kind of hard, especially trying to play football in the Philadelphia area,” Runyan said. “People were always giving me these unfair comparisons against my dad when I was just a 14-year-old kid just trying to find my way. I didn’t even know what position I was good at yet. It was really difficult and I still get those comparisons to him. I feel like sometimes they’re unfair.”

Being drafted because of his talents and not his father’s legacy, Runyan said, will be a huge accomplishment.

“I feel like I’m at the point where my whole life I’ve been living kind of in the shadow, but I’m trying to step outside that shadow and cast a bigger one over that one,” he said.

Runyan said he remembers going to watch his dad’s games with the Eagles, but he doesn’t have many vivid memories of actually seeing his father play.

“I never really watched him,” he said. “I’d always watch the ball. Donovan McNabb, Brian Westbrook, guys like that, because they’re the show. My mom was talking to me one time, and I was like, ‘Mom, don’t you watch the ball?’ and she said, ‘No, I don’t watch the ball at all. I just watch your dad.’ ”

Not everyone was impacted or awestruck by Dad's career in the spotlight.

“I didn’t really appreciate the fact he played football because that was normal to me,” wide receiver Michael Pittman Jr. of USC said of his father, a running back for 11 NFL seasons. “I thought everybody’s dad played football.”

Pittman said that even now, his dad doesn’t talk football all that much, even though three of his sons play at a high level.

“He’s just focused on raising us as kids and he doesn’t really talk about himself and talk about his past achievements,” he said. “He’s never really put pressure on us. He just lets us play. He’s never forced us to play football. He’s never made us go run routes, go work out. He just lets us work.”

And then there is Alabama cornerback Trevon Diggs. His father was not an NFL player, but his brother Stefon is one of the top receivers in the league as well as a father figure to Trevon. Their father, Aron, died in 2008.

“He’s like my dad, honestly,” Trevon said of Stefon, who is only four years older. “He was there for me when my father passed, so he has always taken care of me. I always ask him everything, no matter what. Two o’clock in the morning, I’m asking him questions.”

Sometimes they are questions about plays. Sometimes they are questions about life.

“He was kind of young at the time, too,” Trevon said. “He was just getting into high school, I want to say. Over time, he started to mature and see that I needed someone. I’m his little brother, so he’s been there for me to help out . . .  You never know with kids that lose a parent. They go missing and things like that. He was there to step up for me. I appreciate that. I thank him as a man for doing it.”

As this next generation of players arrives in the NFL, they’ll not only be continuing on in the family business but benefiting from the experience and wisdom that have come with such a history.

“He's been through a lot and seen a lot, so he has answers for everything,” Thaddeus Moss said of his father. “And this [draft] process itself, it's nothing new. Nothing’s changed. I'm leaning on him during this time because he has the answers to everything . . .  He's given me advice from A to Z.”

It’s what dads do.

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