Unmarried, own a house together...who claims deductions?



I just got my Form 1098, which is a mortgage interest statement.
Although both our names appear on it, the Taxpayer's Federal ID # is
just lists MY Social Security number.

Does this mean *I*, and only *I* can claim this interest as a deduction
on my taxes, or am I supposed to split it between me and my girlfriend?
Actually, the same question applies to claiming real estate taxes.
Both our names are on the house, so does this mean I have to split the
taxes between us, or can I just claim them alone?

The obvious advantage is one person claiming everything. Using a
simple example:

ME
$10,000 mortgage deduction
$3,000 real estate tax deduction
=$13,000 total

HER
=$5,000 standard deduction

TOTAL
$18,000 in deductions
----

Splitting all the interest and taxes between us:

ME
$5,000 mortgage deduction
$1,500 real estate tax deduction
=$6,500 total

HER
$5,000 mortgage deduction
$1,500 real estate tax deduction
=$6,500 total

TOTAL
$13,000 in deductions

Obviously, the first scenario is better...but is it legal?
So...basically, two questions:

A) Do we have to split the mortgage interest deduction? (Even though
only MY Tax ID # appears on the Form 1098.)

B) Do we have to split the real estate tax deductions, or can one of us
claim it all? (Even though we both own the house together.)

Thanks in advance!!

.