Serial and DMA: Question

I’d like to use DMA to get the data from the serial RX FIFO into RAM.
My Question: If I setup a DMA, does the DMA wait until data is available, or does it finish as soon as no data is in the FIFO?

Let’s say I want to receive 1kB of serial data.
Can I setup a BDP for 1kB, then start DMA and just wait until the “full” bit is set in the BDP?
Or do I have to wait for the FIFO full interrupt and then setup a DMA for only the 32 bytes of the FIFO?