Well, it could be just new lower branches forming off the trunk, unless it's below a graft line.

I think that some rootstocks are more prone to put out sucker growth than others, but that's just a guess. I've got some trees that do it a lot, some that don't do it all, and it doesn't seem to correlate with how well the tree is doing. I get it more with in-ground citrus. I take it as evidence that the roots are getting the proper water/nutrients and the tree is getting enough light/proper temperatures and so can expend energy on growth--even though it's not exactly where I want it. Maybe it has something to do with comparative vigor or age of the tree? I am not sure.

Lately I have been letting the suckers get a little length to them and then have been trying to root them--working on getting my own rootstock this way.

SJN, if the growth (below the graft line) are suckers, they need to be removed..otherwise they'll take energy needed for the tree itself..the longer u keep it on the more energy it takes.
I too notice some of my trees are more likely getting suckers and they come off as soon as I see them. Just pluck w/finger and thumb.
The longer you leave on the plant, the better chance the trunk will scar when you remove it. Also, the scar will be larger..Toni

Another alternative is let the suckers grow to a pencil size and graft another tree in it about 5 inches from the mother plant. That way you have a new plant growing very cheap way of doing it.
That's what I did to my matured plum. Now I have 3 different trees in one. The good thing about it is you don't need a ladder to harvest the fruit. They are shoulder high.

Ben, I've a question..did you graft on the suckers while they were on the mom tree? Didn't this weaken the state of the mom if you did? That's interesting..Toni

Toni:
Oh, this suckers usually grow straight from the base of the mother tree and usually has its own roots and if you disengage this from the mother plant you have a new tree ready to be planted or sometimes in my case this suckers grow about a foot from the base so as I said cut the suckers maybe about 6 inches and graft it from there. My mistake on my first try was graft a new tree at the end of these suckers because my scion is only 1/4" diameter and I matched the same diameter of the sucker whereI grafted it so it was a long stick sticking up and at the end of that stick are new flowers emerging. Now, the stem before the graft new branches emerging so it is taking all the sap that is intended to the new grafted tree. You don't want that. You want the whole nutrients supply the new tree. So I end up tearing all the new branches that emerged before the graft.
And I graft a lot. So you see now a bunch of flowers in full bloom right now at the ends of those suckers.
No, actually when you graft you are cutting the suckers'energy and hopefully transfer that energy to the new plant. You hope that more nutrients will supply the new pllant so it will be just as big as the mother plant. If it gets too big then you can prune it.
The reason for grafting is to have another fruit grow to the existing one.

Thanks for all the great advice. The suckers are well below the graft lines on the trees. I was wondering about if they could be used for grafting or rooting (thanks for answering that for me.) I didn't even think about scar lines, makes alot of sense though. I plan to 'experiment with grafting this year, I have been doing some reading, and hope to try it soon. Thanks again
~SJN

I have a trifoliate as the rootstock. I grafted a calamondin in one branch 2 years ago and let 2 trifol to grow. The cal is now over 3 feet and flowering lots. Just 2 weeks ago I grafted a Kishu and a Willowleaf mandarin to the other 2 tri branches.
I am going to take pictures of my 2 trees I was describing and post it here. Interested?

Ben, yes, I'm interested in sseeing your pics. CAn you somehow mark where you grafted by adding lines/circles areound the area? I'm still not sure I understand..LOL. Sorry.

I don't know how to add lines or circles in a digital pictures.

sjn:
Go to this webpage and take a look T-budding simplified with pictures:

http://aggie-horticulture.tamu.edu/citrus/budding/budding.htm

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Satsuma plum grafted on the suckers of a santa rosa plum on right picture. The mother tree is on the left.
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A close up view of the grafted branches. Santa rosa plums are all vegetative but the satsuma is in full bloom.
I just grafted a yellow plum at the tip of the satsuma. See the cellophane?