Exterior of rental home A Starwood Waypoint rental property in Orlando, one of about 82,000 that will be under the combined company’s ownership.

DALLAS—Among single-family rental landlords, the post-merger Invitation Homes will overshadow the current top dog, American Homes 4 Rent (AMH), by more than half. It will control about 82,000 rental properties, compared to the 49,000 now owned by AMH.