A query against MOSS search engine returns a specified number of results and a indication of the total number of results. When working with the API this is the TotalRows property of the ResultsTable, working with the WebService this is the TotalAvailable element of the ResponsePacket.
If you, like me, want to base your paging on the TotalRows or TotalAvailable properties and you expect it to return the exact number of results you're in for some strange behaviour...
I do not have a nice solution yet, although the API also exposes the IsTotalRowsExact property. This will tell you when you're on the save side. The webservice ResponsePacket has not got an equalivant property.
The MSDN documentation of the API does not mention this number not being exact: http://msdn2.microsoft.com/en-us/library/microsoft.office.server.search.query.resulttable_members.aspx
The webservice documentation actually does mention it: http://msdn2.microsoft.com/en-us/library/aa193748(office.11).aspx#RangeType_TotalAvailable
"The total number available. This number may not be 100% accurate and all these results may not be accessible."
The number will become more accurate once you move to the end of the resultset.
Be warned...