Cats are considered fully grown at 1 year old. After this, any growth may be the result of overeating and weight gain.
Cats reach maturity relatively quickly, being considered mature once they reach 12 months of age. After this point, cats are considered juniors until about 2 years of age. During the junior years cats may still make a lot of mistakes and be quite active. In human terms, junior cats are living through their teens and early 20s. It is not until they reach 3 years old that cats enter the prime of their lives as adults.
Growth wise, cats stop getting bigger around the 1-year mark. When they are first born, kittens are no bigger than the palm of the human hand. At the end of the first week, their weight should have doubled. By 1 month old, kittens are big enough to sit up and play. They transition to solid food at 2 months and lose their milk teeth at 3 months. In human years, 3-month-old kittens would be about 4 to 5 years old.
At 6 months of age, kittens are old enough to be on their own without their mother. Once fully grown the cat should be about 28 inches long and between 5 to 20 lbs. in weight.