To ensure that this relationship is maintained correctly, you should change the account running SQL Server only through the Properties tab of the SQL Server Properties in Enterprise Manager.
When you install the Microsoft Search Service, this relationship will be set up correctly. However, the account running SQL Server must be an administrator of the Microsoft Search Service. The Microsoft Search Service is external to SQL Server, and it will run in the context of the local system account. Although you can have many SQL Server instances running on a single computer, you can have only one instance of the Microsoft Search Service on any computer. Microsoft Search Service is a component that is installed during a typical installation. Microsoft Search Service is an external service to SQL Server that must be installed in order to perform full-text searches. A SQL Server index is always and immediately updated to reflect changes that happen to the data they represent, whereas, in most cases, a full-text index must be explicitly rebuilt to reflect any changes to the data. Due to the fact that SQL Server does not maintain full-text indexes, they do not behave like SQL Server indexes. Even so, their number is limited per server, not database you are limited to a maximum of 256 full-text catalogs per server. Many indexes can be in one catalog, but they must all be from the same database, because a catalog cannot span databases. The Microsoft Search Service maintains a series of files that comprise the full-text indexes in full-text catalogs. In addition to performing the searches, the Microsoft Search Service also maintains, populates, and builds the full-text indexes.