Not clear on what PQgetResult does

I don't understand in what sense PQgetResult is asynchronous.  Obviously 
PQsendQuery returns immediately and apparently PQgetResult() allows me 
to get separate results from multiple queries submitted together, but...

Let's say I have a table with 1,000,000 rows and I PQsendQuery() a query 
to get them all.  When I call PQgetResult() the first time, will it 
block until all 1,000,000 are ready, or will it send back everything 
that's ready at the time I call it?

If the latter, is pgtcl's pg_getresult supposed to work the same way?