Hi Donna,
If they look mature enough to have harvest-able fruit by the end of the growing season, I would leave them and enjoy the free fruit/Volunteers.

This is one of my Compost Piles:

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Assuming you are making compost to feed your garden, they aren't robbing anything! :-] And if you leave them, you will a)eat the fruit and return the trimmings to the pile for another round and b) add the plants to the compost at the end of the season for another round. Nothing to lose here!

If you think you have enough growing days left for them to reach maturity for harvest you could leave them. In my zone I wouldn't bother with the tomatoes, but the potatoes have potential yet as they can overwinter & grow again in spring. I've transplanting sprouting potatoes with success, so if you want to move them so you can use the rest of the pile sure.

Also, if blight is a concern in your area the self sown nightshade vegs harbor it, so control by removing all of them.

I've actually found that volunteer tomatoes seem to be happier and more disease resistant than the ones I plant. I have blight out the wazoo.

I really doubt I'll be able to get anything from the plants. Neither have blooms yet and it's getting late in the season. I will let them live til they die of natural causes (frost) but they are very nice plants and look much nicer than the ones in the garden. Jon, OMG! That is one fabulous compost heap!!

I have a 3 bin, wooden pallet compost system. In the bin containing mature compost, some sort of tomato volunteer geminated earlier in the summer. Over the course of the summer, I encouraged its growth with an occasional watering. Now I have an enormous plant absolutely loaded with fruit. Early blight has been a huge problem for my tomato crop this year but that particular plant has no sign of it. My second bin, adjoined to the third, is the active one now and its temperature is running close to 150. With it producing so much heat, it will be interesting to see how the tomato growing bin fairs this fall when the weather cools.