I've just always left them alone as they never seemed to branch out or pose a problem...Eventualy they will flower from those areas.
I wouldn't worry about them.

Thank you floridays. I really appreciate you easing my worries. Here I thought I may have a papaya tree with branchs every few inches. LOL

I planted these tree almost two years ago, Jan on this year we had a freeze (28 degrees). The whole top of my trees froze and completely turned brown. All I had was the trunk after all the leaves and fruits fell off. I figured I had nothing to lose so I trimmed the top off completely, so I had left was a 5 Ft, bald trunk. Several weeks later new growth appeared. This is what the tree looks like now 7 months later...I guess you can trim these pretty severely and still grows and fruit...

Freeze Jan '08 (all the fruits fell off also)
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Taken today, More than I know what to do with
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What a great save puglvr1! Thank you for the closeup pictures of your trees so I can see where the fruit comes out from and how large my little tree will have to get before it will produce any fruit. What kind of fertilizer do you use? Mine is growing in a pot so I can take it inside during the winter.

Thanks orchidcrazy! Since you have yours potted, I would recommend Dynamite Slow Release Fertilizer, it is recommended for pots also and you can apply it once and lasts up to 9 months. Or Osmocote works well also. I have a link below you can check them out. H. Depot and Wally World carries some of them. Good luck with yours...Click on the container to get more info.

Here is a link that might be useful: Dynamite Plant Fertilizers

Do you use the palm and citrus Dynamite or the all purpose?