Source: Wikipedia (yeah, I know) - last updated 2016 so may not be 100% accurate.

List of health systems they operate:

AMITA Health, Illinois
Ascension Calumet Medical Center, Chilton, Wisconsin
Ascension DePaul Services, San Antonio
Ascension Mercy Medical Center, Oshkosh, Wisconsin
Ascension Michigan, Warren, Michigan
Ascension Providence, Mobile, Alabama
Ascension St. Elizabeth Hospital, Appleton, Wisconsin
Brighton Hospital, Brighton, Michigan
Centro San Vicente, El Paso, Texas (community health center)
Columbia St. Mary's Hospital, Milwaukee
Lourdes Hospital, Binghamton, New York
Providence Healthcare Network, Waco, Texas
Sacred Heart Health System, Pensacola, Florida
Saint Agnes Hospital, Baltimore, Maryland
Saint Thomas Health, Nashville, Tennessee
Seton Healthcare Family, Austin, Texas
St. John Health System, Tulsa, Oklahoma
St. Vincent Health, Indiana
St. Vincent's HealthCare, Jacksonville, Florida
St. Vincent's Health System, Birmingham (Blount, Oneonta, East, and Pell City), Alabama
Via Christi Health, Wichita, Kansas

Source: Wikipedia (yeah, I know)

List of health systems they operate:

AMITA Health, Illinois
Ascension Calumet Medical Center, Chilton, Wisconsin
Ascension DePaul Services, San Antonio
Ascension Mercy Medical Center, Oshkosh, Wisconsin
Ascension Michigan, Warren, Michigan
Ascension Providence, Mobile, Alabama
Ascension St. Elizabeth Hospital, Appleton, Wisconsin
Brighton Hospital, Brighton, Michigan
Centro San Vicente, El Paso, Texas (community health center)
Columbia St. Mary's Hospital, Milwaukee
Lourdes Hospital, Binghamton, New York
Providence Healthcare Network, Waco, Texas
Sacred Heart Health System, Pensacola, Florida
Saint Agnes Hospital, Baltimore, Maryland
Saint Thomas Health, Nashville, Tennessee
Seton Healthcare Family, Austin, Texas
St. John Health System, Tulsa, Oklahoma
St. Vincent Health, Indiana
St. Vincent's HealthCare, Jacksonville, Florida
St. Vincent's Health System, Birmingham (Blount, Oneonta, East, and Pell City), Alabama
Via Christi Health, Wichita, Kansas