I _know_ I'm missing a simple query here, probably using sys.partitions (actually, just found it. Doh! sys.dm_db_partition_stats), but I needed to know the size of a partition before and after adding several columns. So...
@schema_name = 'dbo'
, @object_name = 'my_staging' --then after adding fields
, @index_id = NULL
, @partition_number = 290
, @data_compression = 'row'
It gave me the size of that particular partition. In retrospect the DMV is probably faster/stronger/better, but this worked in a pinch.