should mutual funds be in my name....or parents?

my mom recently gave me a little over 10K to invest in mutual finds. since neither one of us knows much about the subject i've been doing a lot of online research. i have a question that perhaps some of you may be able to answer. after living in the US for quite some time my parents will be permanently moving to Colombia in about a month. they won't be working there (just living off the rents from some properties they own there) but i know they'll still have to file their taxes every year in the US. my question is, should i put the mutual funds under my name or my mom's? who'll end up paying more taxes on the long run for it or does it add up the same? am i making sense? my reasoning is that since they'll probably be making less per year than me once they move they might not tax it as much.
PS these are the funds that i'll probably end up investing in:
Vanguard Index
Vanguard Total Intl Stock Index
Third Avenue Small-Cap Value
Harbor Bond
Alpine Realty Income & Growth Y
i'm under the impression that unlike a CD for example investing in a mutual fund allows you more flexibility in that you can cash out whenever you want...or i can keep reinvesting in the fund and then take money as needed in the future...please correct me if i'm wrong. thanks.

neptune77,

Any person may give a gift of up to $12,000 per year tax free. That means your mom wouldn't have to pay taxes on the gift she was still below this limit including all the gifts she gave to anyone else during that calendar year. You would be required to pay ordinary income taxes on that amount for the year it was received unless you contributed it to a tax sheltered account.

If you have a 401k at work, you could match the amount your employer adds to your account. Next max out a Roth IRA by contributing the $4,000 limit for 2006 (for single with AGI less than 110k). If you have any remaining, throw the rest of the money into one of your employer sponsored 401k funds even though you have surpassed the match. The limit for 401k contributions each year is above $10,000.

You are not required to pay income tax on a gift you've received. Tax was paid on these funds when the gifter earned it.

And, just to clarify, any person may give $12,000 per year per person. This is not an accumulative number. If neptune77's mother wanted to give $12k each to him, his spouse, his seven children, each of his five siblings, the nice man next door, the UPS guy, her manicurist, me, Al Gore, and her paperboy, there would be no gift tax on any of it.