Let's suppose a CPU wants to make a DMA read transfer from a PCI Express device. Communication to PCI Express devices is provided by transaction layer packets (TLP). Theoretically, the maximum payload size is 1024 doubleword for TLP. So how does a DMA controller act when a CPU gives a DMA read command to PCI Express device in size of 4 megabyte?
In the PCIe enumeration phase, the maximum allowed payload size is determined (it can be lower then the device's max payload size: e.g. a intermediate PCIe switch has a lower max. payload size).
Most PCIe devices are DMA masters, so the driver transfers the command to the device. The device will send several write packets to transmit 4 MiB in xx max sized TLP chunks.
A PCI based bus has no "DMA Controller" in form of a chip or a sub circuit in the chipset. Every device on the bus can become a bus master. The main memory is always a slave.
Let's assume you have build your own PCIe device card, which can act as an PCI master and your program (running on CPU) wants to send data from that card to main memory (4 MiB).
The device driver knows the memory mapping for that particular memory region from operating system (some keywords: memory mapped I/O, PCI bus enumeration, PCI BARs, ).
The driver transfers the command (write), source-address, destination-address and length to the device. This can be done by sending bytes to a special address inside an pre-defined BAR or by writing into the PCI config space. The DMA master on the cards checks these special regions for new tasks (scatter-gather lists). If so, theses tasks get enqueued.
Now the DMA master knows where to send, how many data. He will read the data from local memory and wrap it into 512 byte TLPs of max payload size (the max payload size on path device <---> main memory is known from enumeration) and send it to the destination address. The PCI address-based routing mechanisms direct these TLPs to the main memory.