The term “batch” has two meanings within TCGA.
A batch as described by the BCRs is a set of related analytes from the same disease that have been distributed to one of the GCCs. Batches can vary greatly in size, but are generally at least half a plate (48 samples). Batches for a disease are numbered sequentially. Batches do not represent any sort of procedural or temporal relationships between the samples other than they all come from the same disease. However, once a participant has been assigned to a batch, subsequent shipments from that participant are assigned the same batch number as the original.
A batch is an alternative term for the serial index used in data archives and MAGE-tab archives. By definition, when naming a data archive, the first number after the level indication is referred to as the serial number. However, this is also informally referred to as the "batch" number because the BCRs use their batch number as the serial number. Centers outside of the BCRs do not necessarily follow this convention and can use the serial number to signify a grouping of samples that are of interest to them. In general, it is unlikely that the batch/serial number used in a data archive has any relationship to the batch number assigned by a BCR.
For more information about batch numbers, see the Batch table of the Code Tables Report.