Unlike a dividend or a capital gain distribution, a return of capital:

NOTE:  A return of capital or principal is more commonly referred to as a Nondividend Distribution.

In order to figure your gain or loss using an average basis:

There are two methods for calculating average basis:

Single-category method:

Double-category method:

Beginning on April 1, 2011, the double-category method will no longer be available for calculating average basis with respect to shares in a mutual fund after that date.  You must use the single-category method for such shares if you choose to use average basis.

No, you may use a different method for shares in a different mutual fund.

If your mutual fund splits, or adjusts its price:

A mutual fund is a regulated investment company that pools funds of investors allowing them to take advantage of a diversity of investments and professional asset management.

You own shares in the fund, but the fund owns assets such as shares of stock, corporate bonds, government obligations, etc. One of the ways the fund makes money for you is to sell these assets at a gain. If the asset was held by the mutual fund for more than one year, the nature of the income is capital gain, which gets passed on to you. These are called capital gain distributions, which are distinguished on Form 1099-DIV (PDF) from other types of income such as ordinary dividends.

Capital gains distribution are taxed as long term capital gains regardless of how long you have owned the shares in the mutual fund.