PCIe DMA transcation to multiple PC RAM slots from FPGA
PCIe can DMA anywhere within the system physical address space, even outside of the local NUMA node, though there will be a performance penalty associated with that. This is all handled exactly the same way the CPU can read or write wherever it likes without needing to know what physical device those addresses correspond to. Accesses from different sources will be time interleaved.

Memory 'filling up' is a higher level concept, this would need to be managed by pointing the DMA engine on the PCIe device to free sections of memory. Generally this is done from within an application or device driver.