A pressurized transport oxy-combustor with different configurations is disclosed. Substantially pure oxygen is fed to the transport oxy-combustor under pressure to combust fossil fuels, generating steam for power generation. The end product is the flue gas containing substantially pure CO2 after moisture condensation. The low excess oxygen necessary to achieve complete combustion in the combustor is scavenged by adding another fuel so that substantially all oxygen fed to the combustor is completely consumed. The capability to operate the transport oxy-combustor as a circulating fluidized bed combustor at very high solids circulation rates makes it unnecessary to use recycled CO2 or flue gas as a means to moderate and control the combustion temperature. The temperature in the combustor is effectively controlled by relatively cooler circulating solids that enter the combustion zone. A small amount of CO2 is recycled for aeration and to convey solids fuel to the combustor.