A creature picks an edge for its tower shield in Pathfinder (also see here). The rules are different for a Dungeons and Dragons 3.5 tower shield (Player's Handbook 123) (30 gp; 45 lbs.):
This massive wooden shield is nearly as tall as you are. In most situations, it provides the indicated shield bonus to your AC. However, you can instead use it as total cover, though you must give up your attacks to do so. The shield does not, however, provide cover against targeted spells; a spellcaster can cast a spell on you by targeting the shield you are holding. You cannot bash with a tower shield, nor can you use your shield hand for anything else.
When employing a tower shield in combat, you take a –2 penalty on attack rolls because of the shield’s encumbrance.
So, yeah, there's no picking an edge in 3.5. Instead, foes simply can't make attacks against a creature that possesses total cover like that provided by a tower shield used this way. (Although because of the tower shield's specificity, casters can still target with spells a creature using a tower shield this way.) So, unless a user has something wacky planned for her second tower shield—sledding, perhaps, or as a replacement after having used the first to block a breath weapon—, there's really no reason to lug it around. (Note that this reader tends to agree that a tower shield is a bad choice.)
Further, just in case it's still relevant, while the tower shield description does say that from it a creature can gain total cover yet the creature "must give up [its] attacks to do so," the Dragon #317 Sage Advice column “Steel, Shields, and Spirits: Official Answers” includes the following exchange:
Total cover prevents any attack against you. You can use a tower shield to get total cover if you give up all your attacks. What does “give up
all your attacks” mean?…
To claim total cover from a tower shield, you must use a standard action. The tower shield rules don’t say that, but that’s what they mean. Since you can take only one standard action each round, you cannot also attack, cast a spell, activate a magic item (except for some use-activated items), use a special ability, use total defense, or start or complete a full-round action during the same round you claim total cover from the shield. You can, however, take a move action before or after you claim cover from the shield.… (101)
The Sage for this column is D&D 3e co-designer Skip Williams. This exchange—which is, in fact, far, far longer than the edited version presented here—is repeated nearly verbatim in the Main FAQ (52) with which some folks take issue.