It depends what you mean by growing. In our solar system, there isn't enough matter around anymore that can fall on planets to make them get noticably larger, but there is stuff raining down on us all the time, mostly dust I guess. So in a sense, I think the earth is very, very slowly getting larger. Do you consider this
"growing?"

The short practical answer is, yes.

A more complete answer follows:
Imagine that we could watch a star+planetary system form.
(This normally takes hundreds of millions of years.)

It is generally believed that planets and their associated star (like our Sun) form during the same time from a very large cloud of gas and dust.Each part of the cloud has mass, so attracts every other part of the cloud by gravity. Some parts of the cloud are denser than others, so have greater gravitational pull. These denser parts are the seeds around which the remaining matter collects to form the planets and the star. The central denser clump will be the star, and the ones farther from the center will be the planets.
The cloud usually has a very slight tendancy to rotate or spin. As the smaller clumps are pulled closer to the big clump, the cloud's spin becomes the revolution of the smaller clumps around the bigger clump (the planet's orbit), and the clumps themselves rotate (the planet's rotation). Once a clump has settled into a well defined
body (the planet or star), it's material doesn't have enough velocity to leave the body, so the body stays about the same size.
When the star becomes dense enough to star shining, it will slowly throw off its material as a hot gas, but this takes many billions of years. The planets may absorb some of this gas, or some stray material from the original cloud or the region of space around the star system, but the amount of this additional material is extremely small. Heat from the star may cause some material from the inner planets to boil off of the planet, but this is also a very small amount. So, practically speaking, the planets stop growing when their material has settled into the neat spheres that you are
familiar with. Some star systems have more than one star. How would you use the above explanation to describe the formation of a binary (two) star system? (Hint: The difference between a planet and a star is in their mass.)