Actually her siblings are part of the problem. She had the parents undivided attention for years and now she doesn't. She is intelligent and looks for ways to gain attention. I am not sure that it is as bad as Rockrose posts based on the few examples given. If she was also doing all of this at school, I would also be a lot more worried. Check out this link on 7 year olds -
http://www.medhelp.org/posts/Child-Behavior/7-year-old-child-is-out-of-control-/show/6364
There are 130 posts. This is not real unusual behavior at this age.
Part of the problem is that taking everything away - just doesn't work. Buy "SOS, Help for Parents," by Lynn Clark. She will give you a system that will work. The following is a post I did for a 6 year old boy. I think you will find it helpful.
"I am sure that at school he gets told "no" and apparently doesn't throw tantrums. So, he does have the ability to control himself. Unfortunately, he has kind of "learned" that his tantrums work for him. This is not that unusual for smart kids. Fortunately, they can usually pretty quickly figure out when things are not going there way - and try something else.
And a 6 year old boy can be a force of nature. I always thought my kindergarten/first grade teachers were absolute Saints for dealing with them.
Oh, do you have any younger kids (say around 2 or 3)? Sometimes these things start as attention getting and escalate. If so, there are a few additional things you can do.
So - do realize that possibly that some of the things you want him to do maybe aren't real easy for a 6 year old. So cut back just a bit (not a lot) on the do's and don't list. Try and redirect when possible.
But mainly don't, "spend a large portion of my day saying "the way you are acting is why we aren't (insert whatever activity here)" and he doesn't seem to get that... " Talking to him just will not work. And talking to him when he is having a tantrum - won't work.
The rule is that when he starts a tantrum - he gets a short timeout. And the timeout does not start until the tantrum stops. He will go nuts for a while. Just keep repeating - "as soon as you choose to stop your tantrum, the timeout will start and 2 min later you can ..." Do not try to reason with him or talk with him while he is yelling. You are just playing into his hands.
Essentially, the rules for behavior modification are that there must be immediate, short, consistent consequences. Do not expect overnight miracles. It has taken him awhile to get to this point and it will take a while to relearn control. But he will.
I would also look into buying "Cool down and work through anger" or "When I feel angry". This is part of a series of books aimed at 4 to 7 year olds and meant to be read to them at night (several times) and then practiced. Kids do need to be taught how to deal with anger. You do not try and use these techniques while he is screaming. But once he stops or later on in the day - you can refer back to them or pull the books back out.
You can find them here - http://www.amazon.com/Cool-Through-Anger-Learning-Along/dp/1575423464/ref=pd_sim_b_5"