Once the grid is full of units, the game will end if the losing player does not have a card they can play to regain control. If a card is removed from the board (i.e. An empty space is created from a card dying), the end game logic resets until the board is full again. A player wins if they hold the majority of tiles on the grid once the game comes to a conclusion.
Another possibility is that when each player is out of cards, the winner will be determined based on who still owns the majority of the grid. If both are tied, with no new cards to play, it is a draw and neither player is the victor.