I did a search on Google for 'tsunami disaster relief', and then had a look at the returned results, both the sponsored results as well as the text matches. Every one I looked at (and I looked at about the dozen top links returned) directed me to contribute to relief funds whose target beneficiaries were unspecified. Yes, they were all relief, but every one of the organisations had a charter far more broad than the disaster whose relief I might want to contribute to.
This is disappointing. I don't donate to the United Way because I'm never sure where my donation will go, nor am I overly pleased with their overhead ratio (admittedly, I researched the overhead several years ago, things might have improved). Instead I usually donate to single-purpose charities whose beneficiaries I specifically want to target.
There are arguments for another approach, of course. A problem inherent in donating to single charities is that high profile problems (notably AIDs, cancer, heart disease) will get the majority of donation, whereas any number of equally (or sometimes more) deserving charities are starved for attention and dollars.
Be that as it may, if I am concerned about where my donation will be used, I wasn't able to develop a comfort level with the tsunami relief funds I found in a brief search.
It seems ironic that those organizations sponsoring ads on Google have had enough time to buy ad space for "tsunami", but not enough time or perhaps inclination to create specific funds that would solicit my interest. But they're happy to use public attention on the tragedy to replenish their general coffers. In a world in which smaller scale tragedies like a single drive-by shooting victim has a charitable fund for their dependents organised through a church or bank, larger organisations should find creation of such targeted funds a simple matter. That is, if they were interested in fulfilling the implied promise of collecting under auspices of a specific named tragedy.