Tom is correct.  In the US, the 205/50R17 is the standard OEM size
for 330i models without sport package, and the 225/45R17 is the
standard OEM size for 325i models with the sport package.  I use both;
the ride is very similar, but the 225/45R17 tires tramline much more.
However, they give much sharper steering response.

IIRC the 225/45 tires are on a 8x17 rim, while the others are on a 7.5x17
rim.

FloydR

..or increased oversteer but anyway...

On the M3 the tyre sizes are larger than other E46s at 225/45 18 on
the front and 255/40 18 on the back so yes I reckon you could easily
go up to those diameters if you wanted.  I reckon there would be an
increase in ride with 17s over 18s depending on your tyre choice.

I'm not sure if you can fit 16s unless they are an option, sometimes
the brakes are too big to fit inside a 16" rim.

If I've understood your question correctly, the 45 figure, the aspect ratio
or profile to use it's more common name, has no affect upon a tyres width,
as it's a percentage of however wide the tyre actually is.

A selection of 17" tyres could have profiles of anything say, between 30 and
80. All having the same width. The only difference between them would be
that the tyre with the 80 profile would have a greater distance between the
rim and the tread. It would be a taller tyre relative to the width, and have
a larger overall diameter than any of the others with a lower profile.
Mike.

No.  Higher 'profile' numbers result in taller tires, not wider.  The
profile does not tell you anything about the tire's width.  But the
width and the profile combined tell you the sidewall height.

Pete

205, 225, 235, 255, etc. all refer to the cross sectional WIDTH of the tire.
This width is defined by the number, so the TREAD WIDTH is a direct
corelation tyo this number. A tire with a 205 cross section has a tread
width that is narrower than a 225, without any6 regard to the other numbers
that will be present. Larger numbers will result in a wider tire, if the
aspect ratio remains the same, then the sidewall will also be taller.

35, 40, 45, 55, 70, etc., all refer to the Aspect Ratio. The Aspect Ratio is
the height of the sidewall as a percentage of the cross sectiional width. A
205/50 has a sidewall height of 102 mm, a 225/50 will have a sidewall height
of 113 mm. A 265/75 (a common light truck or SUV size) is 265 mm wide with a
sidewall that is 75% (just under 199 mm) of that. A 255/35 will have a tread
width of 255 mm and a sidewall height of 89 mm.

As a practical matter, the numbers generally work out (in the size ranges
that we want to know about for a BMW), that if the RIM diameter increases 1
inch, the aspect ration will be reduced 5%, if the cross sectional width
remains unchanged. A 225/55x15, a 225/50x16 and a 225/45x17 are all
equivelent. I suppose this would be true of all tire sizes, but I've not
actually done the math to know for sure.

In this example, the 15 is the smallest tire and the 17 is the largest, but
the difference is only 7 revolutions per mile, so the effect on gearing,
speedometer accuracy, power band, etc., will be insignificant. The 17 makes
the most accurate speedo output -- I know this from first hand experience.
My car when the cruise is set to 85 on the speedo, passes the mile markers
with astounding repeatability in a time that says the car is doing 83.7 mph.
The Trip Computer also reports a number that is the same, as near as I can
carry a decimal place.