A question that any new immigrant would ask sooner or later is, "Is Canada still under United Kingdom Rule?, or is Canada controlled by any other country?". The answer is NO.

Up to 1931, UK had significant political control over Canada. Full legislative autonomy was granted to Canada by the Statute of Westminster, 1931, passed by the United Kingdom and ratified by the Canadian parliament. In 1982, the Canada Act terminated the power of the British parliament's ability to legislate for Canada, and the authority to amend the constitution was transferred to Canadian legislative authorities.  Therefore, Canada does not pay taxes to UK, and neither does UK has any legislative power over Canada.

So that being cleared, lets find out why people even ask the question  "Is Canada still under United Kingdom Rule?". It is because of the Monarchy of Canada. Canada has a head of state not elected through a voting system. Since Canada is a Commonwealth realm, Elizabeth II is the monarch. since  Elizabeth II is the queen of UK, this gives the impression that Canada is controlled by UK. There is no provision in Canadian law requiring that the king or queen of Canada must be the same person as the king or queen of the United Kingdom; Canada has complete sovereignty as an independent country and the Queen's role as monarch of Canada is separate from her role as the British monarch or the monarch of any of the other Commonwealth realms. So the conclusion? Canada does have a monarchy, which has zero influence from UK or any other country.

Lets touch on the powers of the monarchy a little bit. First of all, Canadians do not pay any money to the Queen or any other member of the Royal Family, either towards personal income or to support royal residences outside of Canada.Normally, tax dollars pay only for the costs associated with the governor general and ten lieutenant governors as instruments of the Queen's authority, including travel, security, residences, offices, ceremonies, and the like.

The monarch is, in theory, the supreme governor of each of the Commonwealth realms, charged with issuing executive orders, commanding the military forces, and creating and administering laws. However, each country now operates under the Westminster system of parliamentary democracy and the concept of responsible government, meaning that the monarch only exercises her powers on the advice of her Crown ministers, who are usually drawn from, and thus responsible to, the elected lower house of the relevant parliament.

Neither she nor her viceroy, however, participates in the legislative process, save for signifying the Queen's approval to a bill passed by both houses of parliament, known as the granting of Royal Assent, and which is necessary for a bill to be enacted as law.

In my opinion, monarchy has played a very minor role in Canada, Australia, New Zealand, ect who share the same monarchy. But in the age of democracy, do we really need a single person to have any form of reserve powers? I guess no one bothers about this question, because practically the monarchy would not be able to influence Canada politically. Say for example, if the monarchy tries to exercise a decision against Canadians, how can she enforce it? She cannot send UK army against Canada, as UK has no involvement with the Canadian monarchy. Even if she wants to, there are other organizations much more powerful like the UN. In these modern times, it is economical ties that let one country have control over another. In a way, US president has more control over Canada than the monarchy.

http://en.wikipedia.org/wiki/Canada_Act_1982
http://en.wikipedia.org/wiki/Canadian_monarchy