Words like māku and māu can be used to talk about future ownership of a thing. I will have a cup of tea. I will buy a car.

But it can also be used to talk about future ownership of a job or an activity.

For example, I can say: "The job of cleaning the kitchen is mine". That is, I claim ownership of the task of cleaning the kitchen. That job is mine! But I haven't done it yet - the kitchen is still dirty. But I can claim future ownership of the job.