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When you were removed you were almost certainly given papers stating what was happening and why. It is unfortunate that you did not keep them.
Being removed does not always attract a ten year ban, but it may have done. In any case a ten year ban would now have expired. But that does not mean you will be admitted. The UK does not give bans longer than ten years.
It is not true that your record is wiped after ten years. What is true is that you are not asked about refusals more than ten years old. However immigration will still know that you were removed and the fact will be taken into account. A removal is a major obstacle to getting a visa because it shows you have been willing to break immigration law in the past.
Having a daughter in the UK will not help your chances of getting a UK visitor visa as it gives you a reason to stay in the UK after the end of your visa.
By far the easiest way of your getting to see your daughter is to have her and her other parent come and visit you outside the UK.