Just add them to Thunderbird.

File|New|Existing Mail Account…

or Application menu|New Message|Existing Mail Account…

or right-click an account, select Settings then Account Actions|Add Mail Account…

If both IMAP and POP are offered, Thunderbird will take the IMAP choice. You'll have to intervene and enter POP settings by hand.

".....Every time I try to install TB, it continually asks to establish a web-based email presence and account...." (see above)

The question is:

Is Thunderbird an IMAP email server (accessed on-line only)

--or--

is it a desktop application, able to access all types of emails, web-based or not?

it continually asks to establish a web-based email presence

Thunderbird is a native email client. It has got nothing to do with webmail.

Is Thunderbird an IMAP email server

Certainly not. It's an email client, which supports IMAP.

is it a desktop application, able to access all types of emails, web-based or not?

Yes, except webmail.

I merely want to use Thunderbird as a local desktop POP3 email program

Is there anything which prevents you from doing that?

OMG

Does TB reside only on a desktop (or local physical computer), and NOT in the cloud, on an IMAP web-based server in the cloud?? Like Yahoo or GMail??

and contrary to some here, yes TB does access and allow downloaded web-based email--all one has to do is plug in another email server's account info, and one can house all emails from multiple servers in one location. TB allows this setup.

Yahoo, GMail, UReach and similar all are web-based email servers. And all have the ability to house all emails to be downloaded from multiple locations onto its server.

Essentially, the question is, does TB receive--and store--all emails in the cloud--on the web? or, is it a desktop, physical computer software, like POP3?

OMG is right. It would be nice if you had a clue about what you are talking about and knew the difference between an email provider and email client software.

Yahoo, gmail and Hotmail are examples of email providers. Providers have email servers and provider email service. That is why they are called providers.

Email client software like Thunderbird run on your computer and help to connect to your PROVIDER and manage your email service.

POP3 is an inbound email protocol. IMAP and SMTP are another email protocol. You have sure learned a lot of email buzz words. Too bad you cannot use them in context or understand what they are.

POP3 is not a program its a protocol. So is IMAP and SMTP.

Tbird, is a "desktop, physical computer software", an email client that can use POP3, IMAP or SMTP protocol when it connects to a provider's emailserver.

In principal you can say POP downloads the email aand delete it from the emailserver IMAP keep it on the emailserver, gives you a copy to read then sync your actions and folders, deleting, moving etc until you move it to a local folder. SMTP is used when sending an email

Read more about it in Wikipedia. search for IMAP, POP, Webmail.

To airmail--I wished your was the first in line for answers--you could probaby sense my frustration...even though my questions never rose to YOUR standards it seems...nonetheless, there was absolutely no need to denigrate me as a novice user in the process...other prior answers only served to foster confusion.

To Gnospen--thank you very much...YOURS was the most welcome, educational, and appropriate answer..again, thank you.