So I have two unidentified new plants growing pretty fast. They both look like they could be trees. They popped up around 4-6 months ago. They are growing where I don't normally cut the grass and I'm wondering what they actually are and if they are worth keeping around.

If I keep them, I would want to replant them in a suitable place. One is growing kind of under the kids trampoline in the backyard. The other is growing on the side of the house, right next to the brick wall. The leaves for both are different and look like no other tree/shrub/bush around me, or at least with-in a few houses of me.

(Click image for larger view)

Here's the first one. This grew last spring, but died after a month or two from heat. Around March or April I think, I noticed something growing again and left it alone. This is how big it is now.

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Close up of the leaf

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Here is the one in the backyard. This one sprung up about the same time I beleive. Close up of the trunk. I used to have alot of weeds in this spot. I used weed killer safe for grass last year and no more weeds. Now this started growing but it didn't look like weeds. So I left this alone as well.

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Close up of the leaf

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No flowers or berries. Just leaves so far. I have no other weeds in my yard or in my neighbors yards.

Any ideas? Let me know if you need different pictures to help ID it. Thanks