North Carolina (52-8) is the No. 1-seeded team overall in the tournament, which begins Friday.
The Titans (48-8), ranked third nationally by Baseball America, host Columbia (27-19), New Mexico (37-20) and Arizona State (35-20-1) at Goodwin Field. Fullerton, the fifth-seeded team, opens against Columbia at 8 p.m. Friday.
New Mexico features third baseman D.J. Peterson, who is expected to be a first-round draft pick in June. Peterson is hitting .411 with 18 home runs and 70 runs batted in.
UCLA (39-17), ranked eighth, will host San Diego State (31-29), San Diego (35-23) and Cal Poly (39-17) at Jackie Robinson Stadium in its regional. The Bruins open with San Diego State at 6 p.m. Friday.
San Diego third baseman Kris Bryant is projected as a top-five pick in the draft. Bryant is hitting .340 with 31 home runs and 62 RBIs.
If Fullerton and UCLA advance, the two teams will play a best-of-three super regional, starting June 7. The Titans have beaten the Bruins twice this season.
The other regionals are:
At Virginia Tech (38-20), Coastal Carolina (37-21), Connecticut (40-19) and Oklahoma (40-19).
At Virginia (47-10), Army (29-11), Elon (32-28) and North Carolina Wilminghton (37-21).
At North Carolina (52-8), Canisius (42-15), Florida Atlantic (39-20) and Towson (29-28).
At North Carolina State (44-14), Binghamton (30-23), Mississippi (37-22) and William & Mary (37-22).
At South Carolina (39-18), Clemson (39-20), Liberty (34-27) and Saint Louis (41-19).
At Louisville (46-12), Bowling Green (24-29), Miami (36-23), Oklahoma State (39-17).
At Florida State (44-15), Alabama (34-26), Savannah State (33-21), Troy (40-18).
At Indiana (43-14), Austin Peay (45-13), Florida (29-28) and Valparaiso (31-26).
At Vanderbilt (51-19), Eastern Tennessee State (36-22), Illinois (34-18) and Georgia Tech (34-25).
At Mississippi State (43-17) , Central Arkansas (39-20), Mercer (43-16) and South Alabama (42-18).
At Louisiana State (52-9), Jackson State (34-20), Louisiana Lafayette (41-18) and Sam Houston State (37-20).
At Kansas State (41-17), Arkansas (37-20), Bryant (44-16) and Wichita State (39-26).
At Oregon (45-14), Rice (41-17), San Francisco (34-22) and South Dakota State (35-22).
At Oregon State (45-10), Texas A&M (32-27), Texas San Antonio (35-23) and UC Santa Barbara (34-23).
Super regionals (June 7-10): North Carolina champion vs. South Carolina champion; North Carolina State champion vs. Oregon champion; Fullerton champion vs. UCLA champion; Virginia Tech champion vs. LSU champion; Vanderbilt champion vs. Louisville champion; Indiana champion vs. Florida State champion; Virginia champion vs. Mississippi State champion; Kansas State champion vs. Oregon State champion.