If you bought the tree it was probably grafted, and those shoots are probably the root stock. If you'd like to try your had and grafting than you can use those. Otherwise I think you will need a new tree.

The leaves on those shoots indicate it is a peach. Apricots are often grafted onto Lovell, a seedling peach. You now have a peach tree with fruit of unknown quality. If you want another apricot; grafting, budding, or buying another are your options.

Thanks a lot for a quick response. Although, being a newbie, have no idea what you said (except the last sentence) :-), I'll do some research on "root stock" and "grafting". Thanks again.

Oh, got it now. Thanks a lot for the explanation. May I ask a related question? I had a similar story with a cherry tree: it died, I left the offshoot to grow over 6 feet, but it does not have big branches and no fruit (I can post photo if needed). Would it be due to the same problem: the offshoot is of questionable quality?

This post was edited by alekdavis on Thu, Jun 26, 14 at 18:34

Besides replacing the trees it seems you need to also figure out why the trees died. It was a brutal winter for almost the whole nation, but in California these trees should not be winter killed. Please tell us about water, fertilizer, sprays, planting procedures; anything that could help so this does not happen again.

Thank you, milehighgirl. You're right, we had a few harsh frosts and majority of my citrus trees did not make it (even though I covered them overnight and watered them). But the non-citrus ones seem okay. This apricot was an exception. A weird part was that since I planted it, it was developing probably twice as fast as any other tree growing next to it (I have a pomegranate, a fig, two peach trees, a persimmon, etc). I thought that maybe I did not prune it correctly, although I pruned all of them in late winter, and the rest of them seem okay. I did not fertilize much this season (I know, bad, but again, all other trees next to it did well despite). So, this is a bit of a mystery. Another possibility is that maybe the roots reached hard pan (our soil is really bad). I'll check the roots when I dig it out. Thanks again for follow-up. I'm so glad I found this forum. :-)

Most common reason fruit trees die is poor soil drainage. That could be the issue here. If so plant on a mound.

Apricots are usually recommended to be summer pruned in CA, for disease prevention, although it's not supposed to matter as much for a young/new tree.

Agree you should mound/raised bed the tree, best to do with native soil from another place in your yard. Most of CA is hard clay (which part are you?).

If you get another cherry make sure it's self fertile if you don't have another.

Thank you melikeeatplants (and all). I'm in Orangevale (Sacramento County). Yep, clay soil (and resulting poor irrigation) is the major problem (curse?) here. Surprisingly, some of the trees I planted about 3 years ago are still doing well. For the new ones, I started planting them on a slightly raised bed, although, I'm not sure how much it would help, since it's just a couple of inches higher than normal.

I'm still not sure what to do about the cherry. I'll probably submit the question (with a picture) in a different thread.

Thanks again.