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The maximum dexterity is the lowest of the numbers quoted for maximum dexterity of armour or shields..
For example: Tower Shield - Max Dexterity is +2 modifier
Full Plate: +2 Max Dex.
Even if you had a Tower shield and leather armor equipped you would still only have a max dexterity bonus of +2
They do not stack to give more. The lowest figure is the cap for your dexterity based skills and abilities.

Void Dragon |

max dex bonus means that you can only have up to the smallest maximum dex bonus allowed by either your armor or shield. So even if the Tower Shield allows +2 dex and you are also wearing Full Plate which has a max dex of +1 then you only get to add the +1 allowed by full plate (if you have a dex bonus of higher than 1 then it is wasted).

Bearded Ben |

A heavy wooden shield has a Max Dex of "-", which means it doesn't affect your Dexterity bonus at all.
Maximum Dex Bonus: This number is the maximum Dexterity bonus to AC that this type of armor allows. Dexterity bonuses in excess of this number are reduced to this number for the purposes of determining the wearer's AC. Heavier armors limit mobility, reducing the wearer's ability to dodge blows. This restriction doesn't affect any other Dexterity-related abilities.
Even if a character's Dexterity bonus to AC drops to 0 because of armor, this situation does not count as losing his Dexterity bonus to AC.
A character's encumbrance (the amount of gear carried, including armor) may also restrict the maximum Dexterity bonus that can be applied to his Armor Class.
Shields: Shields do not affect a character's maximum Dexterity bonus, except for tower shields.

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So then if the tower shield was made out of lets say mithril it would have a dex bonus max of +4 since anything that is made of mithril for armor is boosted by 2 on its dex bonus max. If you also wear lets say mithril agile breast plate which has a dex bonus of 5,then by wearing both those things you would have a max dex bonus of 4 or did I not calculate that right?

Kayerloth |
@poundpuppy30 - Further note the Max Dex bonus is a limit not an amount you receive. A heavy wooden shield grants a +2 shield bonus to your AC, while the breastplate grants a +6 armor bonus to your AC. Only the breastplate limits the amount of Dex bonus you may apply to your AC and would do so only if you Dexterity was 18 or greater.

Kayerloth |
So then if the tower shield was made out of lets say mithril it would have a dex bonus max of +4 since anything that is made of mithril for armor is boosted by 2 on its dex bonus max. If you also wear lets say mithril agile breast plate which has a dex bonus of 5,then by wearing both those things you would have a max dex bonus of 4 or did I not calculate that right?
Correct, you would be limited by the lesser of the values between your armor or shield which in your example is the tower shield's +4.

Kayerloth |
And the shields with max dex bonus that have a "-' mean they dont affect your bonus at all so then your max dex bonus would be left up to your armor in that scenario right?
Yes that is also correct, keeping in mind that various feats and abilities such as a Fighters Armor Training might also effect your calculations.