The Border mat, a space for tracking gains and trashes each turn. Each player gets one. Every gain goes to Incoming, unless something moves it somewhere else, so cards will come into the deck after Clean-up draw rather than before it, so a bit slower. Every trash goes to Outgoing, to be put in the trash pile start of next turn; they don't interact with effects concerning the trash until then.
Other rules:
- When-gain abilities trigger when the card goes to Incoming. When-trash abilities trigger when the card goes to Outgoing.
- If a card moves off or onto a Border for any reason other than gaining or trashing, it does not count as a gain or trash (like Exile isn't gaining).
- Discarding from Incoming and moving Outgoing to the trash are two separate effects to do once each first thing at start of turn. If Donate is in the game, choose the order you do the three effects in.
- The Border mat is included whenever a card's instructions refer to the "Border", "Incoming" or "Outgoing". I might be persuaded by using a type though.
So, its main purpose is a tracking aid, enabling effects that would otherwise require memory that not everybody has or wants in their games of Dominion. Abilities concerning your own Border are fine, but ones concerning the other players could be an interesting area. Or a card could move around Borders somehow, if that's interesting?
An example:

A
Smugglers that can work on any player, both gains and trashes. The card it gains goes on your Incoming, so all the other players' Smuggler cards can gain a copy of it until your next turn.
I haven't tested any card ideas out for this mechanic, only brainstormed. Your ideas, should you wish to enter, could easily be more interesting than mine.
I will close the contest in 7 days,
January 17th 04:00pm forum time. Until then...