Mechanics of partitioning
Partitioning is only at the table level and is for managing partitions of that table.  Typically the advantage of partitioning is in swapping in and out data and for getting additional control of the granularity of storage and backup.  To some extent it can also help with performance if there are shared partition columns in a join, but that probably shouldn't be a reason to partition.

I understand your thinking about the child tables, but if you want that data also partitioned by country (for some of the above reasons), you would have to add a column because the partition function is restricted.

What is your thinking about why you want to partition in the first place?

http://msdn.microsoft.com/en-us/library/ms190787