Are you referring to Cost Allocation—Help | ArcGIS Desktop ?
It doesn't have an area parameter but it does have a maximum distance parameter, so I am not quite sure how you can limit the allocation to area
Thanks for getting back to me - its the area parameter that I am stuck on. Each point is a settlement and I want to define a polygon around it with an area of 13.4 hectares. However I dont want a simple buffer I want it to be based on the raster friction surface, so I would end up with an irregular line. In other words if there was grassland to the west of the settlement and bogland to the east, the polygon would extend further to the west.
I would have a look at the results without the limitation of area first to see what you get
The only way I can think of offhand is to perform the cost allocation for a location with a limiting distance, then determine the area covered, if too low, increase the limiting distance and repeat