http://i939.photobucket.com/albums/ad234/Qadmus58/IMGP3043.jpg
This one more picture of the tree..

The second one is a type of Prunus - cherry, plum.

First one, I am not sure. Here is the picture of the first one:

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Thank you very much. I am not sure whether I have to remove it or not since it is too close to the strusture.

This looks more like my Japanese anemone, 'Honorine Jobert,' than a tree.

I was thinking Porcelain Berry, in which case you should get rid of it before it takes over the world.

The tree looks like a wild black cherry (small white blooms in spring, with small black berries later). Not the kind you eat. Better dig it up because pruning it back does not kill it, the root system gets bigger so the sooner the better. I have one I need to dig up too.

Thank you all so very much. I think the tree is definitely a wild black cherry (thank you countrygirl!). I will have to dig it out and attempt to move it to another location. The other one is a mystery.

Do prunus have leaves like that? I thought first porcelain berry but it's not vining like one.

My vote is plain old white mulberry..another one for the trash tree pile.

The tree is definitely Prunus - bark and leaves. Not a mulberry.

A friend thinks the other plant is Lavatera. Can you take another photo of it?

Thank you, Carol. Here are more pictures.
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Looks like Cocklebur, Xanthium strumarium...

Here is a link that might be useful: Cocklebur

Then it definately needs to be removed or you will have it everywhere. Which brings to mind a funny true story. I once had an Appaloosa mare, who like some Aps was VERY smart. She could open the gate and let herself and the other horses out. So we had to put a lock on it. Then I noticed she started having cockleburs in her tail and so did my daughters pony. BUT we did not have any cockleburs on our land. At the same time, the two of them would suddenly show up in my front yard instead of in the pasture. So I followed them after about the second time when I put them back in the pasture. There was a tree down over the fence on the back of our property that we didn't know about. They would calmly step over the fence and walk up the hill to a neighbors house, eat to their heart's content, then walk back down the road to come back in the front yard. They were getting the cockleburs in the neighbors field - sometimes they would actually come back through the woods and cross the downned fence. None of the other horses went with them, it must have been a secret....Oh, I really miss that horse! She was one of a kind.

Thank you very much for the nice story. This thing is gone and my wife could not understand why I even kept it this long. As to the tree, it was very tough to gig out even though it is a only a few months old. The roots develop horizontally and are shallow, but still very hard to remove. I had to cut some out. I panicked for a few minutes when I thought I was cutting through the pipes because they look like white PVC. Since I could not get myself to just dump it, I moved it to another location in the back where it cannot bother anything if it survives the shock. I hope it does as it looks pretty. I have no idea what the construction companies do these days. My house is new and I discovered after I started digging and planting that my "soil" is composed of the after-building garbage that was buried on the property. I found plastic gallons, electrical wires, cigarette butts and pieces of wood. They cover that with some grass and a few boxwoods and sell you a house you can call home.