ALTER PARTITION FUNCTION SPLIT is an operation on a Partition Function, and will affect all Partition Schemes using that function, and all tables and indexes residing on those Partition Schemes.
Here's a function to list all the partitions with their boundary values and row counts:
SELECT
tbl.name table_name,
indx.name index_name,
pf.name partition_function,
ps.name partition_scheme,
prt.value boundary_value,
p.partition_number,
prt.boundary_id,
prt.value boundary_value,
p.rows
FROM
sys.tables AS tbl
JOIN sys.indexes AS indx
ON indx.object_id = tbl.object_id
JOIN sys.partition_schemes ps
ON indx.data_space_id = ps.data_space_id
JOIN sys.partition_functions pf
ON ps.Function_id = pf.Function_id
JOIN sys.partitions p
on p.object_id = indx.object_id
and p.index_id = indx.index_id
LEFT JOIN sys.partition_range_values prt
on prt.function_id = pf.function_id
and prt.boundary_id + case when pf.boundary_value_on_right = 1 then 1 else 0 end = p.partition_number