Multithreaded Delphi database application failing with large amounts of data

Question

Overview of the application:
I have a Delphi application that allows a user to define a number of queries, and run them concurrently over multiple MySQL databases. There is a limit on the number of threads that can be run at once (which the user can set). The user selects the queries to run, and the systems to run the queries on. Each thread runs the specified query on the specified system using a TADOQuery component.

Description of the problem:
When the queries retrieve a low number of records, the application works fine, even when lots of threads (up to about 100) are submitted. The application can also handle larger numbers of records(150,000+) as long as only a few threads (up to about 8) are running at once. However, when the user is running more than around 10 queries at once (i.e. 10+ threads), and each thread is retrieving around 150,000+ records, we start getting errors. Here are the specific error messages that we have encountered so far:

a: Not enough storage is available to complete this operation
b: OLE error 80040E05
c: Unspecified error
d: Thread creation error: Not enough storage is available to process this command
e: Object was open
f: ODBC Driver does not support the requested properties

Evidently, the errors are due to a combination of factors: number of threads, amount of data retrieved per thread, and possibly the MySQL server configuration.

The main question really is why are the errors occurring? I appreciate that it appears to be in some way related to resources, but given the different errors that are being returned, I'd like to get my head around exactly why the errors are cropping up. Is it down to resources on the PC, or something to do with the configuration of the server, for example.

The follow up question is what can we do to avoid getting the problems? We're currently throttling down the application by lowering the number of threads that can be run concurrently. We can't force the user to retrieve less records as the queries are totally user defined and if they want to retrieve 200,000 records, then that's up to them, so there's not much that we can do about that side of things. Realistically, we don't want to throttle down the speed of the application because most users will be retrieving small amounts of data, and we don't want to make the application to slow for them to use, and although the number of threads can be changed by the user, we'd rather get to the root of the problem and try to fix it without having to rely on tweaking the configuration all the time.