[bhtbijnk] Rook and pawn endgame

Consider a chess variant, played on a board of any size.

Each player starts with some number of pawns and rooks, initially placed so as to make the game interesting.  They play regular chess moves, except pawns promote only to rooks. 

Not sure when the game ends.  Perhaps first promotion.  Perhaps annihilation (all opponent pieces captured).  Perhaps when one player has established a permanent advantage in number of rooks.

The motivation is to capture the feeling of go 囲碁 endgames, with loosely connected subgames (combinatorial game theory).  I read a similar treatment in an article a while back.

What are the strategies?