Do you mind elaborating why a db partitioned like that is not enough for your registration example? If the partitioning is based on the email address, then you know where the new user's email has to be if exists, you don't need to query all partitions.
For example, following your partitioning logic, if the user registers as [email protected], we'd need to query only partition j.
For example, following your partitioning logic, if the user registers as [email protected], we'd need to query only partition j.