What is the object of preposition in English grammar?

What is its grammar explanation?How different between object and object of preposition?

prepositional phrases describe a noun or verb. They are used for "color" in writing. The prepositional phrase consist of the preposition, the object, and maybe some modifiers of the object.

What is the object (of preposition (in English Grammar))?

I have underlined the object in each phrase.

My cat is in the tree.

The car went through the fence.

My niece is in Northern Texas.

The Governer spoke a gaffe at the Hispanic conference. He should not have made the Mexican joke about beer guzzing, at least, not in a Hispanic convention. I wonder if his fans really think he is suitable for a candidate in the upcoming election. Such is life, in these times.

So can you identify the prepostions, and see the relationship with its object?