On manned-missions which take its participants further and further into space it will be quite difficult to have a control center on Earth as it takes longer an longer to communicate.
It takes the light around 8 minutes to travel from the surface of the sun to Earth. Without any delay this would be 16 minutes for two-way communication and there's surely a point/zone on/in which it will be impractical to communicate.
Is there research on this topic?
"For missions with 'M' crew members that will take its crew 'X' AU (astronomical unit[s]) away from Earth it is reasonable to have mission control solely on Earth. The crew members are not allowed to make mission-critical decisions on their own"
"For missions with 'M' crew members that will take its crew 'Y' AU away from Earth it is reasonable to have a hybrid-solution. After 'X' AU (...). Crew members should decide democratically."
"For missions with 'M' crew members that will take its crew 'Z' AU away form Earth it is reasonable to have mission control solely in the hands of the crew. It's recommended to base this on a hybrid solution. After 'Y' AU (...). When 'M' exceeds 'N' high ranked members voices count twice."