did you try right clicking on the top bar and see if you have an additional toolbar listed there? if so uncheck it to make it go away. You normally have navigation, bookmark, if you see another one with that name that would be it you can try view then toolbars also to see if it might show there to uncheck. Was it not listed in your add remove programs list?. You might be talking about the google toolbar if so you can choose to hide it or remove it from firefox, I took it off of mine completely. Then to make your url area bigger you can right click up on the top of the bar and choose customize (or click view > toolbars> customize) then you should be able to drag out the url address bar bigger you can also while you have it in the customize state drag the google toolbar part off and into that customize box, that is where you can store various items you can add to your firefox bars. When it is in customize state you can also drag the google toolbar off of the bar with the url address bar and on to the bar below it if you want to have it there instead. Once you are all done moving things just close the customize box and it will lock it in place

Perhaps the IE8 Privacy Mode is what your looking for, DA

With my IE6, if you delete your history etc, that empties the address bar drop down list. If you wish to put some oft used addresses back in the drop down list, you must type those addresses back in the address line. Just visiting the sites wont populate the list

it is not related to firefox that task bar is part of your windows. The Start button then the quick launch buttons etc are not part of firefox. If you right click there near the start button for example and then go to toolbars there you will see the option for address, that one has to be checked for the address bar to appear on the task bar. But if you have installed SP3 on your xp computer then the address bar option is no longer listed, do you have SP3 on your pc? If so that is when you lost your address bar option. This is how most are going about getting it back "Enable any other toolbar on the Task Bar... (i.e. The Quick Launch Bar) then, drag it to the top of the screen (off the taskbar onto desktop). Once the top of the screen has a toolbar, right click it and viola... you now have the ability to choose Address Bar. If you want the Address Bar on the bottom task bar, simply drag its handle to the Taskbar and adjust (and lock toolbars)." another method 1. rightlcick desktop toolbar -> toolbars -> quick launch 2. unlock the toolbar 3. leftclick and hold the quicklanch section and slide it to the rightside of the desktop and allow it to dock there 4. rightclick that rightside docked toolbar -> toolbars -> address 5. Done or "Drag My Computer up to the top of your screen, it creates a bar and from there you can right click and add address bar. Now, right click again and remove My Computer from this bar, now you're left with just address." If you find that when you try to drag the address toolbar back onto the task bar it does not survive a reboot then you will need to leave it docked either at the top of the screen or right above the taskbar on the desktop. there is a freebie app that you can get which will do what you want I think and is much easier than doing hacks or all that dragging. Freeware - Address Bar for XP SP3, Open Last Closed Tab, and More : MuvEnum Software if any of those don't work let me know