What is the ruling on a landowner partnering with a contractor to build a house, with the contractor bearing all costs and the two splitting the profit after the sale? Is this considered Mudarabah, Shirka, or a compound contract?

This transaction is a partnership between two parties: one provided the land, and the other provided the cost of construction and labor. If it is permissible to participate with 'urūd (assets other than cash, like land), then the land must be appraised to determine the share of its owner. This scenario is considered a "Mudarabah that includes a partnership" or "Ibda‘" (a form of partnership where one partner works voluntarily on behalf of the other's share). The general principle in transactions is permissibility, and it seems this scenario is permissible if it is said that participation with 'urūd is allowed.