Rett Varner spent the first part of Tuesday afternoon sitting at his parents' table staring at the computer screen. He spent the second half of the day jumping for joy.

With the 197th overall pick, the Marlins selected the University of Texas-Arlington right-handed pitcher in the sixth round. Varner became the second Maverick taken in the Draft, joining teammate Michael Choice, who was the 10th overall selection in the first round by the Oakland Athletics. Teammates Jason Mitchell (15th round, Royals) and Logan Bawcom (17th round, Dodgers) were also selected to mark a historic day in UT-Arlington baseball history.

Draft Central

This year marked the first time in school history that four players were selected in the top 20 rounds of the Draft. In the 1981 Draft, four Mavericks players were taken between the 22nd and 27th rounds.

"Our school has always been a factory for putting out good talent, and it's nice for the school to get recognition and our program to be recognized," Varner said. "I think it show guys in the area that they don't have to go to a big school to get exposed if they want to play on the next level."

Last season, Verner paced the team by going 8-5 with a 3.56 ERA in 103 2/3 innings. An honorable mention All-Southland Conference selection, he posted three complete games in 2010 and made nine starts pitching at least seven innings, including six of his past seven.

Verner credits Choice for keeping UT-Arlington's name in the national spotlight.

"We didn't just have area scouts at our games, we had cross-checkers and scouting directors there, too," he said. "He gave us a lot of exposure that maybe we would not have had. I owe him a steak dinner before we all leave."

Since 1973, there have been 90 Draft or free-agent selections from the UT-Arlington baseball program. There have been 43 picks during that span, including Adam Moore (Seattle, '06), Hunter Pence (Houston, '04), Mark Lowe (Seattle, '04), Ryan Roberts (Toronto, '03) and John Lackey (Angels, '99).

Add Varner to the list.

Here's a look at the rest of the Marlins' Day 2 picks:

Round 2, Robert Rasmussen, LHP, UCLA: Rasmussen has four pitches he's around the plate with, though he does need to be a little more efficient with his pitches. He's a bit undersized.

Round 3, Jacob Realmuto, INF, Carl Albert H.S.: Named Big All City Player of the Year in Oklahoma.

Round 4, Alvin Toles, OF, Sandy Creek H.S.: The son of former NFL linebacker Alvin Toles, this center fielder has above-average speed and an above-average arm.

Round 5, Robert Morey, RHP, University of Virginia: The junior went 9-3 with a 3.72 ERA in 15 starts.

Round 7, Mark Canha, OF, University of California: He has above-average raw power and average speed.

Round 8, Alan Oaks, RHP, University of Michigan: An All-Big 10 third-team selection, he compiled a 6-5 record with a 3.82 ERA

Round 9, Austin Brice, RHP, Northwood H.S.: He throws in the low-to-mid 90s mph range and is raw.

Round 10, Aaron Senne, IF, University of Missouri: Named the co-Big 12 Conference Player of the Year after batting .400 with 16 home runs and 59 RBIs in 55 games.

Round 11, Grant Dayton, LHP, Auburn University: He won eight games and sported a 4.36 ERA.

Round 12, James Wooster, OF, Alvin CC: Is a 6-foot-1, 200-pound right fielder who was named the team's Most Valuable Player.

Round 13, Kentrell Dewitt, OF, Southeastern CC

Round 14, Daniel Black, INF, University of Oklahoma: He was named first-team North California All-American and first team Golden Valley All-Conference as a freshman.

Round 15, Ryan Fisher, OF, Irvine: At 6-foot-3, 200 pounds, he has good speed and raw power.

Round 16, Randy LeBlanc, RHP, Covington HS: Considered one of the top 200 high school prospects in the country.

Round 17, Zachary Neal, RHP, University of Oklahoma: He went 13-0 and helped lead Howard College to the NJCAA National Championship with a 63-1 overall mark in 2009.

Round 18, Corey Goudeau, RHP, Frank Phillips College: Has developed over the past two years after not being recruited out of high school.

Round 19, Dallas Poulk, INF, State University: He was an All-American as a freshman in 2007 and has steadily developed as a steady hitter.

Round 20, Alfredo Lopez, INF, Compton CC: He hit .414 and was selected a first-team All-American by the California Community College Baseball Coaches Association.

Round 21, Kenneth Toves, LHP, University of New Mexico: He played his first two years in junior college and went 2-0 in 19 appearances as a sophomore.

Round 22, Jeremy Heatley, RHP, University of Arkansas: The 6-foot-2, 215-pounder is a versatile hurler and has been used in the starting rotation or out of the bullpen.

Round 23, Blake Treinen, RHP, South Dakota State: He did not play in 2009 after transferring from University of Arkansas and Baker University.

Round 24, Greggory Glime, C, Baylor University: A leader, he was the team captain in 2009 and 2010.

Round 25, Michael Ojala, RHP, Rice University

Round 26, Todd Muecklisch, INF, Lewis-Clark State College

Round 27, Brandon Cunniff, RHP, Cal. St.

Round 28, Charles Keefer, C, U. of Louisiana-Lafayette

Round 29, Viosergy Rosa, INF, Odessa College

Round 30, Zach Robertson, LHP, University of Iowa